Factor this trinomial completely. $20 x ^ { 2 } - 33 x y + 10 y ^ { 2 }$
A) (4 x $-$ 5 y )(5 x + 2 y )
B) (4 x + 5 y )(5 x $-$ 2 y )
C) (4 x $-$ 5 y )(5 x $-$ 2 y )
D) (4 x + 5 y )(5 x + 2 y )
E) not factorable

Question

Quizplus · Accepted Answer

To factor the trinomial, we need to look for two binomials that multiply to give us the trinomial. We can start by looking at the factors of the first term, 20x^2, and the factors of the last term, 10y^2. The factors of 20x^2 are (1x, 20x^2), (2x, 10x), (4x, 5x), (5x, 4x), (10x, 2x), and (20x^2, 1x). The factors of 10y^2 are (1y, 10y^2), (2y, 5y), and (5y, 2y).

We can see that the only combination of factors that will give us the middle term, -33xy, is (4x, 5y) and (5x, -2y), which gives us:

(4x - 5y)(5x - 2y)

Therefore the answer is C.

Factor This Trinomial Completely 20x2−33xy+10y220 x ^ { 2 } - 33 x y + 10 y ^ { 2 }20x2−33xy+10y2

Factor This Trinomial Completely $20 x ^ { 2 } - 33 x y + 10 y ^ { 2 }$