Question

4(x^2+2x+5)^2+17(x^2+2x+5)(x^2+6x)+4(x^2+6x)^2 factors

Answer 1

Answer:

let x^2+2x+5=m,x^2+6x=n

then, 4m^2+17mn+4n^2

=4m^2+16mn+mn+4n^2

=4m(m+4n)+n(m+4n)

=(m+4n) (4m+n)

=(x^2+2x+5+4x^2+24x) (4x^2+8x+20+x^2+6x)

=(5x^2+26x+5)(5x^2+24x+20)

=(5x^2+25x+x+5)(5x^2+24x+20)

={5x(x+5)+1(x+5)} (5x^2+24x+20)

=(x+5)(5x+1)(5x^2+24x+20)