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Questions and Answers
Factorize (x + 3) (x + 3) using a suitable identity.
Factorize (x + 3) (x + 3) using a suitable identity.
(x + 3) (x + 3) = (x + 3)^2
Use the identity (x + a) (x + b) = x^2 + (a + b) x + ab to find the product (x + 3) (x + 7).
Use the identity (x + a) (x + b) = x^2 + (a + b) x + ab to find the product (x + 3) (x + 7).
(x + 3) (x + 7) = x^2 + (3 + 7) x + (3 * 7) = x^2 + 10x + 21
Find the square of (b - 7) using identities.
Find the square of (b - 7) using identities.
(b - 7)^2 = b^2 - 14b + 49
Simplify (a^2 - b^2) using identities.
Simplify (a^2 - b^2) using identities.
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Evaluate 712 using identities.
Evaluate 712 using identities.
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Study Notes
Factorization of Quadratic Expressions
- Factorizing (x + 3)(x + 3) can be done using the identity (a + b)^2 = a^2 + 2ab + b^2, where a = x and b = 3.
- (x + 3)(x + 3) = x^2 + 2*3x + 3^2 = x^2 + 6x + 9.
Product of Binomials
- The product of two binomials (x + a) and (x + b) is given by the identity (x + a)(x + b) = x^2 + (a + b)x + ab.
- Using this identity, we can find the product (x + 3)(x + 7) = x^2 + (3 + 7)x + 3*7 = x^2 + 10x + 21.
Squaring of Binomials
- The square of a binomial (a - b) can be found using the identity (a - b)^2 = a^2 - 2ab + b^2.
- Using this identity, we can find the square of (b - 7) as (b - 7)^2 = b^2 - 2*7b + 7^2 = b^2 - 14b + 49.
Difference of Squares
- The difference of two squares a^2 - b^2 can be simplified using the identity a^2 - b^2 = (a + b)(a - b).
- This identity can be used to simplify expressions involving the difference of squares.
Applications of Identities
- Identities can be used to evaluate numerical expressions, such as 7^2 using the identity a^2 = a*a.
- For example, 712 can be evaluated as 7*7 = 49.
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Description
Test your skills by using suitable algebraic identities to expand the given products and find the results. Practice expanding algebraic expressions with this quiz.
