Question

Factor each expression completely.

Answer 1

$Use:\\a^2-b^2=(a-b)(a+b)\\(a\pm b)^2=(a^2\pm2ab+b^2\\==============================\\27.\\18z^2-8=2(9z^2-4)=2\left[(3z)^2-2^2\right]=2(3z-2)(3z+2)\\\\29.\\2a^2-16a+32=2(a^2-8a+16)=2(a^2-2a\cdot4+4^2)=2(a-4)^2\\=2(a-4)(a-4)\\\\31.\\12x^2+36x+27=3(4x^2+12x+9)=3[(2x)^2+2\cdot2x\cdot3+3^2]\\=3(2x+3)^2=3(2x+3)(2x+3)$

$33.\\3x^2-24x-27=3(x^2-8x-9)=3(x^2+x-9x-9)\\=3[x(x+1)-9(x+1)]=3(x+1)(x-9)\\\\35.\\-x^2+5x-4=-(x^2-5x+4)=-(x^2-x-4x+4)\\=-[x(x-1)-4(x-1)]=-(x-1)(x-4)\\\\37.\\x^2-y^2=(x-y)(x+y)\\\\39.\\-6z^2-600=-6(z^2+100)$