Question

Part A: Factor 2x2y2 + 6xy2 + 18x2y2. Show your work.

Part B: Factor x2 + 10x + 25. Show your work.

Part C: Factor x2 − 36. Show your work.

Answer 1

Answer:

A.

$2xy^2(10x+3)$

B.

$(x+5)^2$

C.

$(x-6)(x+6)$

Step-by-step explanation:

Part A. The expression $2x^2y^2+6xy^2+18x^2y^2$ consists of three terms: $2x^2y^2,\ \ 6xy^2,\ \ 18x^2y^2$ The first and the last terms are like terms, we can add them:

$2x^2y^2+18x^2y^2=20x^2y^2$

Now,

$20x^2y^2=2xy^2\cdot 10x\\ \\6xy^2=2xy^2\cdot 3$

So,

$2x^2y^2+6xy^2+18x^2y^2=2xy^2(10x+3)$

Part B. The expression $x^2+10x+25$ is a square of $x+5,$ so

$x^2+10x+25=(x+5)^2$

Part C. Use the difference of squares formula:

$x^2-36=x^2-6^2=(x-6)(x+6)$