Question 1

Apply the distributive property to simplify the expression $$x(9x^2 + 5$$)$$. What is the result?

Accepted Answer

$$9x^3 + 5x$

Question 2

Which of the following expressions correctly applies the distributive property to $$z(4y^2 - 7$$)$$?

Accepted Answer

$$4y^2z - 7z$

Question 3

A chemist needs to distribute $$a(b^2 + 3b$$)$$ in a formula. What is the simplified result?

Accepted Answer

$$ab^2 + 3ab$

Question 4

Which step is necessary to simplify $$m(2m^2 + 8$$)$$ using the distributive property?

Accepted Answer

Multiply $$m by $$each term inside the parentheses

Question 5

A biologist models population growth with $$k(5n^2 - 2n$$)$$. What is the expanded form?

Accepted Answer

$$5kn^2 - 2kn$

Question 6

Simplify the expression $$t(7t^2 + 4t - 1$$)$$ using the distributive property.

Accepted Answer

$$7t^3$$ + $$4t^2 - t$

Question 7

Which of the following is the correct expansion of $$a(2a^2 + 3a + 6$$)$$?

Accepted Answer

$$2a^3$$ + $$3a^2 + 6a$

Question 8

A medical researcher uses $$p(4q^2 - 5q + 2$$)$$ in a calculation. What is the result after applying the distributive property?

Accepted Answer

$$4pq^2 - 5pq + 2p$

Question 9

Expand and simplify $$y(6y^2 - 3y + 8$$)$$.

Accepted Answer

$$6y^3$$ - $$3y^2 + 8y$

Question 10

Which expression is equivalent to $$r(10r^2 + 7r - 4$$)$$ after applying the distributive property?

Accepted Answer

$$10r^3$$ + $$7r^2 - 4r$

Question 11

A student expands $$s(3s^2 + 2s - 9$$)$$ for a physics problem. What is the correct result?

Accepted Answer

$$3s^3$$ + $$2s^2 - 9s$

Question 12

Expand $$w(8w^2 - 6w + 1$$)$$ using the distributive property.

Accepted Answer

$$8w^3$$ - $$6w^2 + w$

Question 13

Which of the following is the correct expansion of $$q(5q^2 + 4q - 2$$)$$?

Accepted Answer

$$5q^3$$ + $$4q^2 - 2q$

Question 14

A business analyst uses $$x(7x^2 + 2x - 5$$)$$ in a profit model. What is the expanded form?

Accepted Answer

$$7x^3$$ + $$2x^2 - 5x$

Question 15

Expand and simplify $$m(6m^2 - 4m + 3$$)$$.

Accepted Answer

$$6m^3$$ - $$4m^2 + 3m$

Question 16

Which of the following is the correct expansion of $$p(9p^2 + 5p - 8$$)$$?

Accepted Answer

$$9p^3$$ + $$5p^2 - 8p$

Question 17

A student expands $$z(2z^2 + 7z - 3$$)$$ for a chemistry calculation. What is the result?

Accepted Answer

$$2z^3$$ + $$7z^2 - 3z$

Question 18

Expand $$n(5n^2 - 2n + 4$$)$$ using the distributive property.

Accepted Answer

$$5n^3$$ - $$2n^2 + 4n$

Question 19

Which of the following is the correct expansion of $$x(8x^2 + 3x - 6$$)$$?

Accepted Answer

$$8x^3$$ + $$3x^2 - 6x$

The Distributive Property in Algebra

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