What is expand (3x^2+2x-1)^2 ?

The solution to expand (3x^2+2x-1)^2 is 9x^4+12x^3-2x^2-4x+1

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

expand

(3 x^{2} + 2 x - 1)^{2}

9 x^{4} + 12 x^{3} - 2 x^{2} - 4 x + 1

Solution steps

(3 x^{2} + 2 x - 1)^{2}

Apply exponent rule:

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

(3 x^{2} + 2 x - 1)^{2} = (3 x^{2} + 2 x - 1) (3 x^{2} + 2 x - 1)

= (3 x^{2} + 2 x - 1) (3 x^{2} + 2 x - 1)

Distribute parentheses

= 3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 x + 3 x^{2} (- 1) + 2 x \cdot 3 x^{2} + 2 x \cdot 2 x + 2 x (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 2 x - 1 \cdot (- 1)

Simplify

3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 x + 3 x^{2} (- 1) + 2 x \cdot 3 x^{2} + 2 x \cdot 2 x + 2 x (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 2 x - 1 \cdot (- 1) : 9 x^{4} + 12 x^{3} - 2 x^{2} - 4 x + 1

= 9 x^{4} + 12 x^{3} - 2 x^{2} - 4 x + 1

3 x^{3} + 7 x

27 a^{2} - 27 a - 12

4 x x

(2 - i) + (1 + i) - 7 i

What is expand (3x^2+2x-1)^2 ?
The solution to expand (3x^2+2x-1)^2 is 9x^4+12x^3-2x^2-4x+1