Use the Binomial Theorem to expand and simplify the expression. $( 7 a + b ) ^ { 3 }$
A) $343 a ^ { 3 } - 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$
B) $a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$
C) $343 a ^ { 3 } + 147 a ^ { 2 } b - 21 a b ^ { 2 } + b ^ { 3 }$
D) $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } - b ^ { 3 }$
E) $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$

Question

Use the Binomial Theorem to expand and simplify the expression.​ $( 7 a + b ) ^ { 3 }$ ​
A) $343 a ^ { 3 } - 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$
B) $a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$
C) $343 a ^ { 3 } + 147 a ^ { 2 } b - 21 a b ^ { 2 } + b ^ { 3 }$
D) $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } - b ^ { 3 }$
E) $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$

Quizplus · Accepted Answer

The Binomial Theorem for the expansion of $(x + y)^n$ gives us the formula $\sum_{k=0}^{n} \binom{n}{k} x^{n-k}y^k$. Applying this to $(7a + b)^3$, we calculate each term: $343a^3$ from $(7a)^3$, $147a^2b$ from $3 \times (7a)^2 \times b$, $21ab^2$ from $3 \times 7a \times b^2$, and $b^3$ from $b^3$, leading to the expansion $343a^3 + 147a^2b + 21ab^2 + b^3$.

Use the Binomial Theorem to Expand and Simplify the Expression (7a+b)3( 7 a + b ) ^ { 3 }(7a+b)3

Use the Binomial Theorem to Expand and Simplify the Expression $( 7 a + b ) ^ { 3 }$