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

The solution to expand (3x^2+2x+y-2)^2 is 9x^4+12x^3+6x^2y-8x^2+4xy-8x+y^2-4y+4

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

expand

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

9 x^{4} + 12 x^{3} + 6 x^{2} y - 8 x^{2} + 4 x y - 8 x + y^{2} - 4 y + 4

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 x + 3 x^{2} y + 3 x^{2} (- 2) + 2 x \cdot 3 x^{2} + 2 x \cdot 2 x + 2 x y + 2 x (- 2) + y \cdot 3 x^{2} + y \cdot 2 x + yy + y (- 2) - 2 \cdot 3 x^{2} - 2 \cdot 2 x - 2 y - 2 (- 2) : 9 x^{4} + 12 x^{3} + 6 x^{2} y - 8 x^{2} + 4 x y - 8 x + y^{2} - 4 y + 4

= 9 x^{4} + 12 x^{3} + 6 x^{2} y - 8 x^{2} + 4 x y - 8 x + y^{2} - 4 y + 4

\frac{3}{20} \div \frac{2}{5}

7 x^{2} - 28 x

i^{4} - 5 i^{3} - 4 i - 1

x^{2} - y^{2} + x + y

x^{2} - y^{2} + x - y

What is expand (3x^2+2x+y-2)^2 ?
The solution to expand (3x^2+2x+y-2)^2 is 9x^4+12x^3+6x^2y-8x^2+4xy-8x+y^2-4y+4