Question

Which binomial is a factor of 9x2 + 24xy + 16y2?

Answer 1

Option A

The binomial factor is 3x + 4y

Solution:

We have to find the binomial factor of given equation

Given equation is:

$9x^2+24xy+16y^2$

Let us factor the given expression

$9x^2+24xy+16y^2$

$\mathrm{Rewrite\:}9\mathrm{\:as\:}3^2\\\\=3^2x^2+24xy+16y^2\\\\\mathrm{Rewrite\:}16\mathrm{\:as\:}4^2\\\\=3^2x^2+24xy+4^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\3^2x^2=\left(3x\right)^2\\\\=\left(3x\right)^2+24xy+4^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\4^2y^2=\left(4y\right)^2$

$=\left(3x\right)^2+24xy+\left(4y\right)^2\\\\\mathrm{Rewrite\:}24xy\mathrm{\:as\:}2\cdot \:3x\cdot \:4y\\\\=\left(3x\right)^2+2\cdot \:3x\cdot \:4y+\left(4y\right)^2\\\\ \mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=3x,\:b=4y\\\\=\left(3x+4y\right)^2\\\\\rightarrow (3x+4y)^2 = (3x+4y)(3x+4y)$

Thus the binomial factor is 3x + 4y

Thus Option A is correct