Find the indicated products by using the shortcut pattern for multiplying binomials. (5 $-$ 4 x )(8 $-$ 5 x )
A) $40 - 25 x + 20 x ^ { 2 }$
B) $40 - 57 x + 4 x ^ { 2 }$
C) $40 + 57 x + 20 x ^ { 2 }$
D) $40 - 57 x + 20 x ^ { 2 }$
E) none of these

Question

Quizplus · Accepted Answer

Use the FOIL (First, Outer, Inner, Last) method, which gives:
$$
\begin{aligned} (5 {-} 4x)(8 {-} 5x) &= 5 \cdot 8 + 5 \cdot (-5x) {-} 4x \cdot 8 {-} 4x \cdot (-5x) \ &= 40 {-} 25x {-} 32x {+} 20x^2 \ &= 20x^2 {-} 57x {+} 40 \end{aligned}
$$
Thus, the answer is D, which matches the simplified result of FOIL.

Find the Indicated Products by Using the Shortcut Pattern for Multiplying