What is expand (16-8x^{1/2}+x)^2 ?

The solution to expand (16-8x^{1/2}+x)^2 is x^2-256x^{1/2}-16x^{3/2}+96x+256

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expand (16-8x^{1/2}+x)^2

expand

(16 - 8 x^{\frac{1}{2}} + x)^{2}

x^{2} - 256 x^{\frac{1}{2}} - 16 x^{\frac{3}{2}} + 96 x + 256

Solution steps

(16 - 8 x^{\frac{1}{2}} + x)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(16 - 8 x^{\frac{1}{2}} + x)^{2} = (16 - 8 x^{\frac{1}{2}} + x) (16 - 8 x^{\frac{1}{2}} + x)

= (16 - 8 x^{\frac{1}{2}} + x) (16 - 8 x^{\frac{1}{2}} + x)

Distribute parentheses

= 16 \cdot 16 + 16 (- 8 x^{\frac{1}{2}}) + 16 x - 8 x^{\frac{1}{2}} \cdot 16 - 8 x^{\frac{1}{2}} (- 8 x^{\frac{1}{2}}) - 8 x^{\frac{1}{2}} x + x \cdot 16 + x (- 8 x^{\frac{1}{2}}) + xx

Simplify

16 \cdot 16 + 16 (- 8 x^{\frac{1}{2}}) + 16 x - 8 x^{\frac{1}{2}} \cdot 16 - 8 x^{\frac{1}{2}} (- 8 x^{\frac{1}{2}}) - 8 x^{\frac{1}{2}} x + x \cdot 16 + x (- 8 x^{\frac{1}{2}}) + xx : x^{2} - 256 x^{\frac{1}{2}} - 16 x^{\frac{3}{2}} + 96 x + 256

= x^{2} - 256 x^{\frac{1}{2}} - 16 x^{\frac{3}{2}} + 96 x + 256

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((3 x^{3} + 5 y)^{2})^{2}

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\frac{p ( x )}{( x ^{2} + 1 ) ( x - 3 )}

What is expand (16-8x^{1/2}+x)^2 ?
The solution to expand (16-8x^{1/2}+x)^2 is x^2-256x^{1/2}-16x^{3/2}+96x+256