What is expand 3(3x^2+2x-6)^2 ?

The solution to expand 3(3x^2+2x-6)^2 is 27x^4+36x^3-96x^2-72x+108

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expand 3(3x^2+2x-6)^2

expand

3 (3 x^{2} + 2 x - 6)^{2}

27 x^{4} + 36 x^{3} - 96 x^{2} - 72 x + 108

Solution steps

3 (3 x^{2} + 2 x - 6)^{2}

(3 x^{2} + 2 x - 6)^{2} = 9 x^{4} + 12 x^{3} - 32 x^{2} - 24 x + 36

= 3 (9 x^{4} + 12 x^{3} - 32 x^{2} - 24 x + 36)

Distribute parentheses

= 3 \cdot 9 x^{4} + 3 \cdot 12 x^{3} + 3 (- 32 x^{2}) + 3 (- 24 x) + 3 \cdot 36

Apply minus-plus rules

+ (- a) = - a

= 3 \cdot 9 x^{4} + 3 \cdot 12 x^{3} - 3 \cdot 32 x^{2} - 3 \cdot 24 x + 3 \cdot 36

Simplify

3 \cdot 9 x^{4} + 3 \cdot 12 x^{3} - 3 \cdot 32 x^{2} - 3 \cdot 24 x + 3 \cdot 36 : 27 x^{4} + 36 x^{3} - 96 x^{2} - 72 x + 108

= 27 x^{4} + 36 x^{3} - 96 x^{2} - 72 x + 108

(q + r^{2} - y^{2})^{2}

\frac{k}{s ( s + 2 )}

zy (z = e^{x + y} + e^{x - y})

\frac{s}{( s - 2 ) ^{3}}

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

What is expand 3(3x^2+2x-6)^2 ?
The solution to expand 3(3x^2+2x-6)^2 is 27x^4+36x^3-96x^2-72x+108