What is expand (3x^2-5x+3)^2 ?

The solution to expand (3x^2-5x+3)^2 is 9x^4-30x^3+43x^2-30x+9

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expand (3x^2-5x+3)^2

expand

(3 x^{2} - 5 x + 3)^{2}

9 x^{4} - 30 x^{3} + 43 x^{2} - 30 x + 9

Solution steps

(3 x^{2} - 5 x + 3)^{2}

Apply exponent rule:

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

(3 x^{2} - 5 x + 3)^{2} = (3 x^{2} - 5 x + 3) (3 x^{2} - 5 x + 3)

= (3 x^{2} - 5 x + 3) (3 x^{2} - 5 x + 3)

Distribute parentheses

= 3 x^{2} \cdot 3 x^{2} + 3 x^{2} (- 5 x) + 3 x^{2} \cdot 3 - 5 x \cdot 3 x^{2} - 5 x (- 5 x) - 5 x \cdot 3 + 3 \cdot 3 x^{2} + 3 (- 5 x) + 3 \cdot 3

Simplify

3 x^{2} \cdot 3 x^{2} + 3 x^{2} (- 5 x) + 3 x^{2} \cdot 3 - 5 x \cdot 3 x^{2} - 5 x (- 5 x) - 5 x \cdot 3 + 3 \cdot 3 x^{2} + 3 (- 5 x) + 3 \cdot 3 : 9 x^{4} - 30 x^{3} + 43 x^{2} - 30 x + 9

= 9 x^{4} - 30 x^{3} + 43 x^{2} - 30 x + 9

8 x^{2} + 10 x

\frac{x ^{2} + 11 x + 24}{x ^{2} + 2 x - 3}

5^{0} \cdot \frac{5 ^{7}}{5 ^{5}}

\frac{1 - cos ^{2} ( x )}{sec ^{2} ( x ) - 1}

What is expand (3x^2-5x+3)^2 ?
The solution to expand (3x^2-5x+3)^2 is 9x^4-30x^3+43x^2-30x+9