What is expand (2x^2-x+5)^2 ?

The solution to expand (2x^2-x+5)^2 is 4x^4-4x^3+21x^2-10x+25

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expand (2x^2-x+5)^2

expand

(2 x^{2} - x + 5)^{2}

4 x^{4} - 4 x^{3} + 21 x^{2} - 10 x + 25

Solution steps

(2 x^{2} - x + 5)^{2}

Apply exponent rule:

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

(2 x^{2} - x + 5)^{2} = (2 x^{2} - x + 5) (2 x^{2} - x + 5)

= (2 x^{2} - x + 5) (2 x^{2} - x + 5)

Distribute parentheses

= 2 x^{2} \cdot 2 x^{2} + 2 x^{2} (- x) + 2 x^{2} \cdot 5 - x \cdot 2 x^{2} - x (- x) - x \cdot 5 + 5 \cdot 2 x^{2} + 5 (- x) + 5 \cdot 5

Simplify

2 x^{2} \cdot 2 x^{2} + 2 x^{2} (- x) + 2 x^{2} \cdot 5 - x \cdot 2 x^{2} - x (- x) - x \cdot 5 + 5 \cdot 2 x^{2} + 5 (- x) + 5 \cdot 5 : 4 x^{4} - 4 x^{3} + 21 x^{2} - 10 x + 25

= 4 x^{4} - 4 x^{3} + 21 x^{2} - 10 x + 25

- 4 (- 6)

(8 x)^{- 2}

11 x^{13}

\frac{3. 9 ^{2} - 16}{3.9 - 4}

What is expand (2x^2-x+5)^2 ?
The solution to expand (2x^2-x+5)^2 is 4x^4-4x^3+21x^2-10x+25