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

The solution to expand (2x^2-x-3)^2 is 4x^4-4x^3-11x^2+6x+9

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

expand

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

4 x^{4} - 4 x^{3} - 11 x^{2} + 6 x + 9

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

2 x^{2} \cdot 2 x^{2} + 2 x^{2} (- x) + 2 x^{2} (- 3) - x \cdot 2 x^{2} - x (- x) - x (- 3) - 3 \cdot 2 x^{2} - 3 (- x) - 3 (- 3) : 4 x^{4} - 4 x^{3} - 11 x^{2} + 6 x + 9

= 4 x^{4} - 4 x^{3} - 11 x^{2} + 6 x + 9

\frac{1}{20}

\frac{- 10}{10}

- \frac{5}{3} + (- \frac{3}{7})

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

(2 y - 5)^{3}

What is expand (2x^2-x-3)^2 ?
The solution to expand (2x^2-x-3)^2 is 4x^4-4x^3-11x^2+6x+9