What is expand ((2(x+h)-5)^2-(2x-5)^2)/h ?

The solution to expand ((2(x+h)-5)^2-(2x-5)^2)/h is 8x+4h-20

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expand ((2(x+h)-5)^2-(2x-5)^2)/h

expand

\frac{( 2 ( x + h ) - 5 ) ^{2} - ( 2 x - 5 ) ^{2}}{h}

8 x + 4 h - 20

Solution steps

\frac{( 2 ( x + h ) - 5 ) ^{2} - ( 2 x - 5 ) ^{2}}{h}

Expand

2 (x + h) - 5 : 2 x + 2 h - 5

= \frac{( 2 x + 2 h - 5 ) ^{2} - ( 2 x - 5 ) ^{2}}{h}

Factor

(2 x + 2 h - 5)^{2} - (2 x - 5)^{2} : 2 h (4 x + 2 h - 10)

= \frac{2 h ( 4 x + 2 h - 10 )}{h}

Cancel the common factor:

h

= 2 (4 x + 2 h - 10)

Distribute parentheses

= 2 \cdot 4 x + 2 \cdot 2 h + 2 (- 10)

Apply minus-plus rules

+ (- a) = - a

= 2 \cdot 4 x + 2 \cdot 2 h - 2 \cdot 10

Simplify

2 \cdot 4 x + 2 \cdot 2 h - 2 \cdot 10 : 8 x + 4 h - 20

= 8 x + 4 h - 20

- \frac{16 x}{( x ^{2} - 4 ) ^{2}}

(\frac{x ^{9} y ^{\frac{1}{3}}}{z} + 2 pt) (\frac{x ^{9} y ^{\frac{1}{3}}}{z} - 6 pt)

\frac{( 4 y ^{8} - 1 ) ^{2}}{16 y ^{8}}

(1 - 3 x - 2) (1 - 3 x + 2)

(2 x^{3} + \frac{1}{x})^{10}

What is expand ((2(x+h)-5)^2-(2x-5)^2)/h ?
The solution to expand ((2(x+h)-5)^2-(2x-5)^2)/h is 8x+4h-20