Factor the expression completely. $56 x ^ { 2 } - 29 x y - 40 y ^ { 2 }$
A) $\quad ( 7 x - 8 y ) ( 8 x + 5 y )$
B) $\quad ( 7 x - 8 y ) ( 5 x + 8 y )$
C) $\quad ( 5 x - 8 y ) ( 8 x + 7 y )$
D) $\quad ( 7 x + 8 y ) ( 8 x - 5 y )$

Question

Quizplus · Accepted Answer

To factor the given expression $56x^2 - 29xy - 40y^2$, we look for two numbers that multiply to $56 \times -40 = -2240$ and add to the middle coefficient, $-29$. The numbers -80 and 35 work, since $-80 + 35 = -45$ and $-80 \times 35 = -2240$. We can rewrite the middle term $-29xy$ as $-80xy + 35xy$, giving us $56x^2 - 80xy + 35xy - 40y^2$. Factoring by grouping, we get $8x(7x - 10y) + 5y(7x - 8y)$, which simplifies to $(7x - 8y)(8x + 5y)$.

Factor the Expression Completely 56x2−29xy−40y256 x ^ { 2 } - 29 x y - 40 y ^ { 2 }56x2−29xy−40y2

Factor the Expression Completely $56 x ^ { 2 } - 29 x y - 40 y ^ { 2 }$