Multiply.
-$\frac { 5 } { 9 } x w^ { 8 } \left( 8 x ^ { 2 } w ^ { 9 } + 3 x ^ { 3 } w ^ { 7 } - \frac { 7 } { 6 } \right)$
A) $\frac { 40 } { 9 } x ^ { 3 } w ^ { 9 } + \frac { 5 } { 3 } x ^ { 3 } w ^ { 7 } - \frac { 35 } { 54 }$
B) $\frac { 40 } { 9 } x ^ { 3 } { w } ^{17} + \frac { 5 } { 3 } x ^ { 4 } { w } ^{15} - \frac { 35 } { 54 } xw ^ { 8 }$
C) $\frac { 40 } { 9 } x ^ { 3 } w ^ { 17 } + \frac { 5 } { 3 } x ^ { 4 } w ^ { 15 } - \frac { 7 } { 6 }$
D) $\frac { 40 } { 9 } x ^ { 2 } w ^ { 17 } + \frac { 5 } { 3 } x ^ { 3 } w ^ { 15 } - \frac { 35 } { 54 } x w ^ { 8 }$

Question

Quizplus · Accepted Answer

When multiplying the given expression, each term inside the parentheses is multiplied by $\frac{5}{9}w^8$. For the first term, $8x^2w^9$, the coefficients $8$ and $\frac{5}{9}$ multiply to give $\frac{40}{9}$, and the variables multiply to give $x^2w^{17}$ (since $8+9=17$). For the second term, $3x^3w^7$, the coefficients $3$ and $\frac{5}{9}$ multiply to give $\frac{5}{3}$, and the variables multiply to give $x^4w^{15}$ (since $3+1=4$ and $7+8=15$). For the constant term, $-\frac{7}{6}$, it is simply multiplied by $\frac{5}{9}$ to give $-\frac{35}{54}$, and the variable $w^8$ is carried over since it multiplies the entire expression. This results in the correct answer being option B.

Multiply - 59xw8(8x2w9+3x3w7−76)\frac { 5 } { 9 } x w^ { 8 } \left( 8 x ^ { 2 } w ^ { 9 } + 3 x ^ { 3 } w ^ { 7 } - \frac { 7 } { 6 } \right)95​xw8(8x2w9+3x3w7−67​)

Multiply
- $\frac { 5 } { 9 } x w^ { 8 } \left( 8 x ^ { 2 } w ^ { 9 } + 3 x ^ { 3 } w ^ { 7 } - \frac { 7 } { 6 } \right)$