Rewrite the binomial of the form $( a - b ) ^ { n }$ as $[ a + ( - b ) ] ^ { n }$. Then expand the binomial. Use Pascal's triangle to find the coefficients.
$$\left( p ^ { 2 } - w \right) ^ { 3 }$$
A) $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; p ^ { 6 } - 3 p ^ { 4 } w + 3 p ^ { 2 } w ^ { 2 } - w ^ { 3 }$
B) $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; - p ^ { 6 } + w ^ { 3 }$
C) $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; p ^ { 6 } - w ^ { 3 }$
D) $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 } ; - p ^ { 6 } + 3 p ^ { 4 } w - 3 p ^ { 2 } w ^ { 2 } + w ^ { 3 }$

Question

Quizplus · Accepted Answer

The correct form after rewriting is $\left[ p ^ { 2 } + ( - w ) \right] ^ { 3 }$. Using Pascal's triangle, the coefficients for the expansion of a binomial raised to the power of 3 are 1, 3, 3, 1. Thus, the expansion is $p^6 - 3p^4w + 3p^2w^2 - w^3$.

Rewrite the Binomial of the Form (a−b)n( a - b ) ^ { n }(a−b)n

Rewrite the Binomial of the Form $( a - b ) ^ { n }$