which expression is equivalent to $(4x^{5}+11)^{2}$?\n$16x^{5}+121$\n$16x^{10}+121$\n$16x^{10}+88x^{5}+121$\n…
which expression is equivalent to $(4x^{5}+11)^{2}$?\n$16x^{5}+121$\n$16x^{10}+121$\n$16x^{10}+88x^{5}+121$\n$16x^{25}+88x^{5}+121$
Answer
Explanation:
Step1: Apply the formula $(a + b)^2=a^{2}+2ab + b^{2}$
Here $a = 4x^{5}$ and $b = 11$. So $(4x^{5}+11)^{2}=(4x^{5})^{2}+2\times(4x^{5})\times11 + 11^{2}$.
Step2: Simplify $(4x^{5})^{2}$
Using the power - of - a - product rule $(ab)^n=a^{n}b^{n}$, we have $(4x^{5})^{2}=4^{2}\times(x^{5})^{2}=16x^{10}$.
Step3: Simplify $2\times(4x^{5})\times11$
$2\times4\times11x^{5}=88x^{5}$, and $11^{2}=121$.
Step4: Combine the terms
$(4x^{5}+11)^{2}=16x^{10}+88x^{5}+121$.
Answer:
$16x^{10}+88x^{5}+121$ (the third option)