What is expand (2a^2-a+3)^2 ?

The solution to expand (2a^2-a+3)^2 is 4a^4-4a^3+13a^2-6a+9

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expand (2a^2-a+3)^2

expand

(2 a^{2} - a + 3)^{2}

4 a^{4} - 4 a^{3} + 13 a^{2} - 6 a + 9

Solution steps

(2 a^{2} - a + 3)^{2}

Apply exponent rule:

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

(2 a^{2} - a + 3)^{2} = (2 a^{2} - a + 3) (2 a^{2} - a + 3)

= (2 a^{2} - a + 3) (2 a^{2} - a + 3)

Distribute parentheses

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

Simplify

2 a^{2} \cdot 2 a^{2} + 2 a^{2} (- a) + 2 a^{2} \cdot 3 - a \cdot 2 a^{2} - a (- a) - a \cdot 3 + 3 \cdot 2 a^{2} + 3 (- a) + 3 \cdot 3 : 4 a^{4} - 4 a^{3} + 13 a^{2} - 6 a + 9

= 4 a^{4} - 4 a^{3} + 13 a^{2} - 6 a + 9

a^{4} \cdot a^{2}

\frac{1}{x ^{2} - 4 x + 4} + 2

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

4 x^{3} + 7 x^{2} + 4 x + 7

9 x^{2} y^{7}

What is expand (2a^2-a+3)^2 ?
The solution to expand (2a^2-a+3)^2 is 4a^4-4a^3+13a^2-6a+9