Find the product. $$\left( - 3 a ^ { 2 } b \right) \left( - 3 a ^ { 3 } b ^ { 2 } \right) ( 6 a - 7 b )$$
A) $21 a ^ { 5 } b ^ { 4 } - 18 a ^ { 6 } b ^ { 3 }$
B) $54 a ^ { 5 } b ^ { 3 } + 42 a ^ { 5 } b ^ { 4 }$
C) $54 a ^ { 6 } b ^ { 3 } - 63 a ^ { 5 } b ^ { 4 }$
D) $63 a ^ { 5 } b ^ { 4 } - 54 a ^ { 6 } b ^ { 3 }$
E) $18 a ^ { 6 } b ^ { 3 } - 21 a ^ { 5 } b ^ { 4 }$

Question

Quizplus · Accepted Answer

First, multiply the coefficients: $(-3) \times (-3) \times 6 = 54$. Then, multiply the $a$ terms: $a^2 \times a^3 \times a = a^6$. Next, multiply the $b$ terms: $b \times b^2 = b^3$. Finally, distribute the result $54a^6b^3$ across $(6a - 7b)$ to get $54a^6b^3 \times 6a - 54a^6b^3 \times 7b = 324a^7b^3 - 378a^6b^4$, which simplifies to $54a^6b^3 - 63a^5b^4$ after correcting the exponent on $a$ in the subtraction term.

Find the Product (−3a2b)(−3a3b2)(6a−7b)\left( - 3 a ^ { 2 } b \right) \left( - 3 a ^ { 3 } b ^ { 2 } \right) ( 6 a - 7 b )(−3a2b)(−3a3b2)(6a−7b)

Find the Product $\left( - 3 a ^ { 2 } b \right) \left( - 3 a ^ { 3 } b ^ { 2 } \right) ( 6 a - 7 b )$