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.

Tutors, please sign in to answer this question.

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}

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