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

The solution to expand (3x^2+2y^2-1)^2 is 9x^4+4y^4+6x^2y^2-6x^2+6y^2x^2-4y^2+1

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

expand

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

9 x^{4} + 4 y^{4} + 6 x^{2} y^{2} - 6 x^{2} + 6 y^{2} x^{2} - 4 y^{2} + 1

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 y^{2} + 3 x^{2} (- 1) + 2 y^{2} \cdot 3 x^{2} + 2 y^{2} \cdot 2 y^{2} + 2 y^{2} (- 1) - 1 \cdot 3 x^{2} - 1 \cdot 2 y^{2} - 1 \cdot (- 1) : 9 x^{4} + 4 y^{4} + 6 x^{2} y^{2} - 6 x^{2} + 6 y^{2} x^{2} - 4 y^{2} + 1

= 9 x^{4} + 4 y^{4} + 6 x^{2} y^{2} - 6 x^{2} + 6 y^{2} x^{2} - 4 y^{2} + 1

2 a^{2} + 5 ab + 2 b^{2}

\frac{8 - 112}{6}

121 - x^{4}

- 49 x^{2}

9 - \frac{5}{2}

What is expand (3x^2+2y^2-1)^2 ?
The solution to expand (3x^2+2y^2-1)^2 is 9x^4+4y^4+6x^2y^2-6x^2+6y^2x^2-4y^2+1