Multiply the expression as you would multiply polynomials. $\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)$
A) $\quad ( a - b ) ^ { 14 }$
B) $\quad a ^ { 38 } - b ^ { 18 }$
C) $\quad (a - b )^ { 5 }$
D) $\quad a ^ { 19 } - b ^ { 9 }$

Question

Multiply the expression as you would multiply polynomials. $\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)$
A) $\quad ( a - b ) ^ { 14 }$
B) $\quad a ^ { 38 } - b ^ { 18 }$
C)  $\quad (a - b )^ { 5 }$
D) $\quad a ^ { 19 } - b ^ { 9 }$

Quizplus · Accepted Answer

This is a difference of squares, so we can apply the formula $(a-b)(a+b)=a^2-b^2$, but in this case the squares are raised to fractional exponents. Using the same idea, we get: 
\begin{align*}
(a^{19/2}+b^{9/2})(a^{19/2}-b^{9/2}) &= (a^{19/2})^2 - (b^{9/2})^2 \
&= a^{19} - b^9.
\end{align*}

Multiply the Expression as You Would Multiply Polynomials (a19/2+b9/2)(a19/2−b9/2)\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)(a19/2+b9/2)(a19/2−b9/2)

Multiply the Expression as You Would Multiply Polynomials $\left( a ^ { 19 / 2 } + b ^ { 9 / 2 } \right) \left( a ^ { 19 / 2 } - b ^ { 9 / 2 } \right)$