What is expand 4(4x^3+2x^2-5x)^2 ?

The solution to expand 4(4x^3+2x^2-5x)^2 is 64x^6+64x^5-144x^4-80x^3+100x^2

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expand 4(4x^3+2x^2-5x)^2

expand

4 (4 x^{3} + 2 x^{2} - 5 x)^{2}

64 x^{6} + 64 x^{5} - 144 x^{4} - 80 x^{3} + 100 x^{2}

Solution steps

4 (4 x^{3} + 2 x^{2} - 5 x)^{2}

(4 x^{3} + 2 x^{2} - 5 x)^{2} = 16 x^{6} + 16 x^{5} - 36 x^{4} - 20 x^{3} + 25 x^{2}

= 4 (16 x^{6} + 16 x^{5} - 36 x^{4} - 20 x^{3} + 25 x^{2})

Distribute parentheses

= 4 \cdot 16 x^{6} + 4 \cdot 16 x^{5} + 4 (- 36 x^{4}) + 4 (- 20 x^{3}) + 4 \cdot 25 x^{2}

Apply minus-plus rules

+ (- a) = - a

= 4 \cdot 16 x^{6} + 4 \cdot 16 x^{5} - 4 \cdot 36 x^{4} - 4 \cdot 20 x^{3} + 4 \cdot 25 x^{2}

Simplify

4 \cdot 16 x^{6} + 4 \cdot 16 x^{5} - 4 \cdot 36 x^{4} - 4 \cdot 20 x^{3} + 4 \cdot 25 x^{2} : 64 x^{6} + 64 x^{5} - 144 x^{4} - 80 x^{3} + 100 x^{2}

= 64 x^{6} + 64 x^{5} - 144 x^{4} - 80 x^{3} + 100 x^{2}

\frac{( x + 1 ) ^{4}}{2}

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

(e^{5 m} - f^{n})^{2}

\frac{2 + 3 x}{( x + 4 ) ( x ^{2} - 5 x + 6 )}

\frac{( 1 - j )}{( 1 + j ) ^{2}}

What is expand 4(4x^3+2x^2-5x)^2 ?
The solution to expand 4(4x^3+2x^2-5x)^2 is 64x^6+64x^5-144x^4-80x^3+100x^2