Combining Like Terms

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Questions and Answers

Which of the following expressions demonstrates the correct application of the distributive property to combine like terms?

$3x^2 + 2x - x^2 + 4 = (3 + 2 - 1)x^2 + 4$
$5ab + 2a^2b - 3ab = (5 + 2 - 3)ab + a^2b$
$7p^2q + 3pq^2 - 2p^2 = (7 + 3 - 2)p^2q$
$4x^2y - 2xy^2 + x^2y = (4 + 1)x^2y - 2xy^2$ (correct)

Which of the following statements correctly describes why $3x^2y$ and $5xy^2$ are not considered like terms?

They contain different variables.
The exponents of $x$ and $y$ are different between the two terms. (correct)
They have different numerical coefficients.
One term has a coefficient of 3, and the other has a coefficient of 5.

If you have the expression $8a^2b - 4ab^2 + 2a^2b + ab^2$, what is the simplified form after combining like terms?

$10a^2b - 3ab^2$ (correct)
$6a^4b^2 - 3a^2b^4$
$10a^2b - 5ab^2$
$6a^2b - 3ab^2$

Which of the following pair of terms are 'like terms'?

$4ab^2$ and $-7b^2a$ (C) Signup and view all the answers

Simplify the following expression by combining like terms: $9p^3 - 3p^2 + 5p^3 + 2p - 7p^2 - p$

$14p^3 - 10p^2 + p$ (B) Signup and view all the answers

Which expression is equivalent to $5x^2y - 3xy^2 + 2x^2y + 6xy^2 - x^2y$ after combining like terms?

$6x^2y + 3xy^2$ (B) Signup and view all the answers

Determine which of the following pairs cannot be combined as 'like terms'.

$7p^2q$ and $7pq^2$ (C) Signup and view all the answers

What is the result of combining like terms in the expression $3a + 4b - 2a + b - 5c$?

$a + 5b - 5c$ (D) Signup and view all the answers

Which of the following expressions is the simplified form of $6x^3 + 2x^2 - 4x^3 + x - 3x^2$?

$2x^3 - x^2 + x$ (D) Signup and view all the answers

What is the simplified form of the expression $7xy + 3x^2 - 2xy + 5x^2 - xy$?

$4xy + 8x^2$ (B) Signup and view all the answers

Which of the following expressions is equivalent to $\frac{1}{2}a^2b + \frac{3}{4}ab^2 - \frac{1}{4}a^2b + \frac{1}{2}ab^2$ after combining like terms?

$\frac{1}{4}a^2b + \frac{5}{4}ab^2$ (A) Signup and view all the answers

Given the expression $5m^2n - 2mn^2 + 3m^2n + mn^2$, what is the simplified result after combining like terms?

$8m^2n - mn^2$ (C) Signup and view all the answers

Simplify the following expression: $10p^2q - 4pq^2 - 2p^2q + 5pq^2 + pq^2$

$8p^2q + 2pq^2$ (B) Signup and view all the answers

Which expression is equivalent to $7ab^2 - 4a^2b + 2ab^2 - a^2b$ after combining like terms?

$9ab^2 - 5a^2b$ (D) Signup and view all the answers

Determine the simplified form of the algebraic expression: $15x - 3y + 7y - 5x + 2z - z$

$10x + 4y + z$ (B) Signup and view all the answers

What is the simplified form of the polynomial $5a^3 - 3ab + 2a^3 + 7ab - 2a^2$?

$7a^3 + 4ab - 2a^2$ (A) Signup and view all the answers

After simplifying the expression $12x^2y - 5xy^2 + 3x^2y + 2xy^2$, what is the coefficient of the $x^2y$ term?

15 (C) Signup and view all the answers

Combine like terms in the expression: $4x^2 - 7xy + 2y^2 - 2x^2 + 3xy - y^2$

$2x^2 - 4xy + y^2$ (C) Signup and view all the answers

What is the sum of the coefficients after simplifying the expression $5a^2b + 3ab^2 - a^2b - 2ab^2$?

7 (B) Signup and view all the answers

Simplify: $2(x^2 + y) - (y - x^2)$

$3x^2 + y$ (C) Signup and view all the answers

Flashcards

Like terms

Terms with the same variables raised to the same powers.

Distributive property

Applying a number to a sum or difference.

Study Notes

Two terms in algebraic expressions are considered "like terms" when they contain the same variable terms raised to the same powers.
Like terms can be combined into one by using distributive properties.
4x²y, 6x²y, and -7x²y serve as examples of like terms as they all have the variables x and y, with x raised to the power of 2.