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Questions and Answers
The process of writing an algebraic expression as a product of factors is known as ______.
The process of writing an algebraic expression as a product of factors is known as ______.
factorisation
A monomial can be expressed as a product of ______ factors.
A monomial can be expressed as a product of ______ factors.
two or more
Common factors of monomials will occur in both ______.
Common factors of monomials will occur in both ______.
monomials
The factors common to both 4xy and 9x are ______ and x.
The factors common to both 4xy and 9x are ______ and x.
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The H.C.F. of monomials is defined as the common factor having the greatest ______ and highest power of the variable.
The H.C.F. of monomials is defined as the common factor having the greatest ______ and highest power of the variable.
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(i) 5y - 15y______
(i) 5y - 15y______
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In the example given, the H.C.F. of 4a³b³ and 12abc is ______.
In the example given, the H.C.F. of 4a³b³ and 12abc is ______.
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Factors of 9x include 1, 9, 3, and ______.
Factors of 9x include 1, 9, 3, and ______.
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(ii) 16m - 4m______
(ii) 16m - 4m______
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To express 8a²b as a product, we can write it as ______ x 4b.
To express 8a²b as a product, we can write it as ______ x 4b.
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(iii) 8x³y² + 8x³______
(iii) 8x³y² + 8x³______
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20x³ - 40x² + 80x______
20x³ - 40x² + 80x______
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X² - 3x²y² - 6xy²______
X² - 3x²y² - 6xy²______
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(2x - 3y)(a + b) + (3x - 2y)(a + b) = ______(a + b)(5x - 5y)
(2x - 3y)(a + b) + (3x - 2y)(a + b) = ______(a + b)(5x - 5y)
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To factorise an algebraic expression, we write it as a product of the binomial and ______ obtained by dividing the expression.
To factorise an algebraic expression, we write it as a product of the binomial and ______ obtained by dividing the expression.
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An algebraic expression with two terms is called a ______.
An algebraic expression with two terms is called a ______.
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The product of H.C.F. of numerical coefficients and the highest common powers of the variables gives the H.C.F. of the ______.
The product of H.C.F. of numerical coefficients and the highest common powers of the variables gives the H.C.F. of the ______.
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To factorise the binomial 3x²y - 6xy², we find the H.C.F. which is ______.
To factorise the binomial 3x²y - 6xy², we find the H.C.F. which is ______.
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For factorization by taking out a common factor, we first find the H.C.F. of all the ______ in an expression.
For factorization by taking out a common factor, we first find the H.C.F. of all the ______ in an expression.
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The H.C.F. of 21 and 35 is ______.
The H.C.F. of 21 and 35 is ______.
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The expression 18x³y² + 36xy - 24x²y³ can be factored as 6xy² ______ (3x² + 6² - 4xy).
The expression 18x³y² + 36xy - 24x²y³ can be factored as 6xy² ______ (3x² + 6² - 4xy).
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The highest common power of x in the monomials 21x³y² and 35x⁵y is ______.
The highest common power of x in the monomials 21x³y² and 35x⁵y is ______.
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For the terms 15a³, -45a², and 150a, the H.C.F. is ______.
For the terms 15a³, -45a², and 150a, the H.C.F. is ______.
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To find the H.C.F. of 2x³y², 10x²y³, and 14x²y², we need to find the H.C.F. of the numerical ______.
To find the H.C.F. of 2x³y², 10x²y³, and 14x²y², we need to find the H.C.F. of the numerical ______.
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A trinomial is an algebraic expression containing ______ terms.
A trinomial is an algebraic expression containing ______ terms.
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To multiply a binomial and a trinomial, each term of the binomial is multiplied with each ______ of the trinomial.
To multiply a binomial and a trinomial, each term of the binomial is multiplied with each ______ of the trinomial.
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For multiplication of a binomial of the type (A + B) and a trinomial (C + D + E), we start by multiplying A by the ______.
For multiplication of a binomial of the type (A + B) and a trinomial (C + D + E), we start by multiplying A by the ______.
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The distributive property is used twice to evaluate (a + b)(c + d) which results in ______ total terms.
The distributive property is used twice to evaluate (a + b)(c + d) which results in ______ total terms.
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A binomial can be expressed as the sum or difference of ______ monomials.
A binomial can be expressed as the sum or difference of ______ monomials.
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When multiplying a monomial with a binomial, we first multiply the monomial with the ______ term of the binomial.
When multiplying a monomial with a binomial, we first multiply the monomial with the ______ term of the binomial.
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If the terms of the binomial are separated by a '+' sign, we ______ the products obtained from each step.
If the terms of the binomial are separated by a '+' sign, we ______ the products obtained from each step.
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In the example of multiplying 2a² and (9b² + 5ab), the result includes terms like 18a²b² and ______ a²b.
In the example of multiplying 2a² and (9b² + 5ab), the result includes terms like 18a²b² and ______ a²b.
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The product of (-3ab) and (7a²c) equals -21a²______
The product of (-3ab) and (7a²c) equals -21a²______
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An algebraic expression is a combination of constants and variables connected by means of four fundamental operations: +, -, x, and ______.
An algebraic expression is a combination of constants and variables connected by means of four fundamental operations: +, -, x, and ______.
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An algebraic expression that has only one term is called a ______.
An algebraic expression that has only one term is called a ______.
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An algebraic expression with two terms is known as a ______.
An algebraic expression with two terms is known as a ______.
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When adding the algebraic expressions -8x² + 6y² + 5 and 2x² - 3y², we combine the like terms to get [-6x² + 3y² + 5]. The like terms are both ______.
When adding the algebraic expressions -8x² + 6y² + 5 and 2x² - 3y², we combine the like terms to get [-6x² + 3y² + 5]. The like terms are both ______.
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In the expression (5x²y) x (-3/5 y²z) x (2xz²), the final product results in -6x⁴______.
In the expression (5x²y) x (-3/5 y²z) x (2xz²), the final product results in -6x⁴______.
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When verifying the equation with x = 1, y = -1, and z = 2, these values are substituted to ______ the expression.
When verifying the equation with x = 1, y = -1, and z = 2, these values are substituted to ______ the expression.
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An algebraic expression having three terms is referred to as a ______.
An algebraic expression having three terms is referred to as a ______.
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Study Notes
Algebraic Expressions
- An algebraic expression combines constants and variables using mathematical operations (+, -, ×, ÷).
- A monomial has one term.
- A binomial has two terms.
- A trinomial has three terms.
Factors of Algebraic Expressions
- Factors are parts of an expression.
- Factorization is representing an expression as a product of its factors.
- Numerical coefficients of factors are multiplied to find the total coefficient.
- Factors of a monomial can be written as a product (e.g., 8a²b = 1 × 8a²b, 8a²b = 2a² × 4b, etc.)
- Common factors are factors common to two or more monomials.
- The highest common factor (H.C.F.) for monomials is the greatest common factor of the coefficients and the highest power of each variable
- Steps to find the H.C.F. of monomials:
- Find the H.C.F. of the numerical coefficients.
- Find the common variables.
- Find the highest common power of each variable.
- Multiply the H.C.F. of the coefficients and the highest common powers of the variables.
Factorisation by taking out a common factor
- Find the highest common factor (HCF) of all terms of the expression.
- Express each term of the expression as a product of HCF and the quotient obtained by dividing each term by HCF.
- Use distributive property to express the given expression as a product of HCF and the sum of the quotients.
- Terms in an algebraic expression will have common factors which can be taken out to make the expression simpler
Multiplication of a monomial and a binomial
- Multiply the monomial by each term of the binomial.
- Add or subtract the products to get the final result.
Multiplication of Binomials
- Use the distributive property twice: (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd
Multiplication of a Binomial and a Trinomial
- Multiply each term of the binomial by each term of the trinomial.
- Combine like terms.
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Description
Test your understanding of factoring algebraic expressions and identifying common factors with this engaging quiz. Dive into terms like monomials, H.C.F., and how to express algebraic forms as products. Perfect for reinforcing key concepts in your Algebra class.
