Question

Part A: Factor x^2^y2 + 6xy^2 + 8y^2. Show your work. (4 points)

Part B: Factor x^2 + 8x + 16. Show your work. (3 points)

Part C: Factor x^2 − 16. Show your work. (3 points)

Answer 1

`A.\\x^2y^2 + 6xy^2 + 8y^2=x^2\cdot y^2+6x\cdot y^2+8\cdot y^2\\\\=y^2(x^2+6x+8)=y^2(x^2+4x+2x+8)\\\\=y^2(x\cdot x+4\cdot x+2\cdot x+2\cdot4)=y^2[x(x+4)+2(x+4)]\\\\=\boxed{y^2(x+4)(x+2)}`


`B.\\x^2 + 8x + 16=x^2+4x+4x+16=x\cdot x+4\cdot x+4\cdot x+4\cdot4\\\\=x(x+4)+4(x+4)=\boxed{(x+4)(x+4)}\\\\or\ use:a^2+2ab+b^2=(a+b)^2\\\\x^2 + 8x + 16=x^2+2x\cdot4+4^2=(x+4)^2=\boxed{(x+4)(x+4)}`


`C.\\x^2-16=x^2-4^2=\boxed{(x-4)(x+4)}\\\\used\ (a-b)(a+b)=a^2-b^2`