Multiply the expression as you would multiply polynomials. $$\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }$$
A) $\quad x ^ { 7 } + 2 x ^ { 7 / 2 } y ^ { 9 / 2 } + y ^ { 9 }$
B) $\quad x ^ { 7 } - 2 x ^ { 7 } y ^ { 9 } + y ^ { 9 }$
C) $\quad x ^ { 7 } + x ^ { 7 } y ^ { 9 } + y ^ { 9 }$
D) $\quad x ^ { 7 } + y ^ { 9 }$

Question

Quizplus · Accepted Answer

When you square a binomial, you use the pattern:
$$(a+b)^2 = a^2 + 2ab + b^2$$
In this case, our binomial is $(x^{7/2} + y^{9/2})$, so when we square it, we get:
$$(x^{7/2} + y^{9/2})^2 = (x^{7/2})^2 + 2(x^{7/2})(y^{9/2}) + (y^{9/2})^2 = x^7 + 2x^{7/2}y^{9/2} + y^9$$
Therefore, the answer is choice A, $x^7 + 2x^{7/2}y^{9/2} + y^9$.

Multiply the Expression as You Would Multiply Polynomials (x7/2+y9/2)2\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }(x7/2+y9/2)2

Multiply the Expression as You Would Multiply Polynomials $\left( x ^ { 7 / 2 } + y ^ { 9 / 2 } \right) ^ { 2 }$