What is expand-4(mx-m+4)^2 ?

The solution to expand-4(mx-m+4)^2 is -4m^2x^2+8m^2x-32mx-4m^2+32m-64

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expand-4(mx-m+4)^2

expand

- 4 (m x - m + 4)^{2}

- 4 m^{2} x^{2} + 8 m^{2} x - 32 m x - 4 m^{2} + 32 m - 64

Solution steps

- 4 (m x - m + 4)^{2}

(m x - m + 4)^{2} = m^{2} x^{2} - 2 m^{2} x + 8 m x + m^{2} - 8 m + 16

= - 4 (m^{2} x^{2} + m^{2} - 2 m^{2} x + 8 m x - 8 m + 16)

Distribute parentheses

= (- 4) m^{2} x^{2} + (- 4) (- 2 m^{2} x) + (- 4) \cdot 8 m x + (- 4) m^{2} + (- 4) (- 8 m) + (- 4) \cdot 16

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - 4 m^{2} x^{2} + 4 \cdot 2 m^{2} x - 4 \cdot 8 m x - 4 m^{2} + 4 \cdot 8 m - 4 \cdot 16

Simplify

- 4 m^{2} x^{2} + 4 \cdot 2 m^{2} x - 4 \cdot 8 m x - 4 m^{2} + 4 \cdot 8 m - 4 \cdot 16 : - 4 m^{2} x^{2} + 8 m^{2} x - 32 m x - 4 m^{2} + 32 m - 64

= - 4 m^{2} x^{2} + 8 m^{2} x - 32 m x - 4 m^{2} + 32 m - 64

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(\frac{n + 1}{2 n + 5}) - (\frac{( n )}{2 n + 3})

\frac{5 ( 3 + 21 )}{6}

What is expand-4(mx-m+4)^2 ?
The solution to expand-4(mx-m+4)^2 is -4m^2x^2+8m^2x-32mx-4m^2+32m-64