16x^2 - 24xy + 9y^2
Select the correct choice below.
(a) 16x^2 - 24xy+ 9y^2=?
(b) The polynomial is prime.
16x^2 - 24xy + 9y^2
Select the correct choice below.
(a) 16x^2 - 24xy+ 9y^2=?
(b) The polynomial is prime.
This polynomial is not prime since it has the factors.
1) Fastest and easiest way to solve this problem is to remember the formula for (a+b)^{2} and observe the pattern.
We know that, a^{2}+2ab+b^{2} =(a+b)^{2}
16x^{2} - 24xy + 9y^{2} = (4x)^{2} - 2.4x.3y + (3y)^{2}
=(4x-3y)^{2}
2) If you do not remember the formula, you can do the factoring the usual way
a.b = 16 x 9 = 144 = 1 x 2 x 2 x 2 x 2 x 3 x 3 = -12 x -12
a+b = -24 = (-12) + (-12)
This gives us two factors of a=-12 and b=-12
16x^{2} - 24xy + 9y^{2}
= 16x^{2} - 12xy -12xy +9y^{2}
= 4x (4x-3y) -3y(4x-3y)
= (4x-3y)(4x-3y)
=(4x-3y)^{2}