Question

What is the following simplified product? Assume x>0 (the > has a line under it)
(sqrt10x^4 -xsqrt5x^2)(2sqrt15x^4 +sqrt3x^3)

A. 10x^4 sqrt6 +x^3 sqrt30x -10x^4 sqrt3 +x^2 sqrt15x

B. 10x^4 sqrt6 +x^3 sqrt30x -x^4 sqrt75 +x^2 sqrt15

C. 10x^4 sqrt6 +x^3 sqrt30x -10x^4 sqrt3 - x^2 sqrt15

D. 10x^4 sqrt6 +x^3 sqrt30x -10x^4 sqrt3 -x^3 sqrt15x

20 points to who can show work and brainliest if I can!

Answer 1

$\left(\sqrt{10x^4} -x\sqrt{5x^2}\right)\left(2\sqrt{15x^4} +\sqrt{3x^3}\right) \\ \\ =2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5} \\ \\ =2\sqrt{25\times6x^8}+x^3\sqrt{30x}-2x\sqrt{25\times3x^6}-x^3\sqrt{15x} \\ \\ =10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

Option D.

Answer 2

The simplified product is; Choice D; 10x^4 sqrt6 +x^3 sqrt30x -10x^4 sqrt3 -x^3 sqrt15x

Polynomial multiplication

(sqrt10x^4 -xsqrt5x^2)(2sqrt15x^4 +sqrt3x^3) can be written mathematically as;

$(\sqrt{10 {x}^{4}} - x \sqrt{5 {x}^{2} } ) \: (2 \sqrt{15 {x}^{4} } + \sqrt{3 {x}^{3} })$

Hence, upon expansion;

• = 2√150x⁸ + √30x⁷ - 2x√75x⁶ - x√15x⁵.

• = 10x⁴√6 + x³√30x - 10x⁴√3 - x³√15x

On this note, the correct choice is Choice D.

Read more on polynomial multiplication;

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