Question

Match the polynomial with its factored form.
__________ a^3-b^3
__________ a^3+b^3
__________ a^2-b^2
__________ a^2+2ab+b^2
__________ a^2-2ab+b^2

A. (a-b)(a-b)
B. (a+b)(a-b)
C. (a+b)(a^2-ab+b^2)
D. (a-b)(a^2+ab+b^2)
E. (a+b)(a+b)

Answer 1

Answer: a^3 - b^3 corresponds to: D. (a-b)(a^2+ab+b^2)

a^3 + b^3 corresponds to: C. (a+b)(a^2-ab+b^2)

a^2 - b^2 corresponds to: B. (a+b)(a-b)

a^2 + 2ab + b^2 corresponds to: E. (a+b)(a+b)

a^2 - 2ab + b^2 corresponds to: A. (a-b)(a-b)

Step-by-step explanation:

a^3 - b^3 corresponds to: D. (a-b)(a^2+ab+b^2)

a^3 + b^3 corresponds to: C. (a+b)(a^2-ab+b^2)

a^2 - b^2 corresponds to: B. (a+b)(a-b)

a^2 + 2ab + b^2 corresponds to: E. (a+b)(a+b)

a^2 - 2ab + b^2 corresponds to: A. (a-b)(a-b)


for explanation, feel free to ask.

Answer 2

Answer:

D. (a - b)(a^2 + ab + b^2) $a^3 - b^3$

C. (a + b)(a^2 - ab + b^2) $a^3 + b^3$

B. (a + b)(a - b) $a^2 - b^2$

E. (a + b)(a + b) $a^2 + 2ab + b^2$

A. (a - b)(a - b) $a^2 - 2ab + b^2$

Step-by-step explanation:

Let's match each polynomial with its factored form:

$a^3 - b^3$ can be factored as $(a - b)(a^2 + ab + b^2)$, the correct match is:

C. (a - b)(a^2 + ab + b^2)

$a^3 + b^3$ can be factored as $(a + b)(a^2 - ab + b^2)$, so the correct match is:

D. (a + b)(a^2 - ab + b^2)

$a^2 - b^2$ can be factored as $(a + b)(a - b)$, so the correct match is:

B. (a + b)(a - b)

4. $a^2 + 2ab + b^2$ is a perfect square trinomial and can be factored as $(a + b)^2$, so the correct match is:

E. (a + b)(a + b) or simply (a + b)^2

5. $a^2 - 2ab + b^2$ is a perfect square trinomial and can be factored as $(a - b)^2$, so the correct match is:

A. (a - b)(a - b) or simply (a - b)^2