Factor.
-$12 x ^ { 2 } + 25 x y + 12 y ^ { 2 }$
A) $( 12 x + y ) ( x + 12 y )$
B) $( 3 x - 4 y ) ( 4 x - 3 y )$
C) $( 3 x + 4 y ) ( 4 x + 3 y )$
D) $( 12 x + 4 y ) ( x + 3 y )$

Question

Quizplus · Accepted Answer

We can solve this quadratic expression by using the FOIL method of multiplication. However, it's quite complex and may take some time. Alternatively, we can try to spot a pattern or shortcut to factorize it. Notice that both the first and last term of the expression contain squares of x and y, respectively. Moreover, their coefficients have a product of 12 and they are both positive. This suggests that we need to factorize the expression using two pairs of binomials, each containing an x and a y term.

The coefficient of xy in the middle term is 25, which means that it's likely that we need two different integers that have a product of 25 and can be combined to give 25 when one is multiplied by 12 and the other by 1. These integers are 3 and 4. We can check that 3 times 4 is 12 and 3 times 1 is 3, and that 4 times 1 is 4 and 4 times 12 is 48.

Therefore, we can write:
$$12 x ^ { 2 } + 25 x y + 12 y ^ { 2 } = ( 3 x + 4 y ) ( 4 x + 3 y )$$

This is the only pair of binomials that results in the original quadratic expression when multiplied using the FOIL method. Hence, the correct answer is Choice C.

Factor - 12x2+25xy+12y212 x ^ { 2 } + 25 x y + 12 y ^ { 2 }12x2+25xy+12y2

Factor
- $12 x ^ { 2 } + 25 x y + 12 y ^ { 2 }$