What is expand (ax^2+bx+c)^2 ?

The solution to expand (ax^2+bx+c)^2 is a^2x^4+b^2x^2+2ax^3b+2ax^2c+2bcx+c^2

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expand (ax^2+bx+c)^2

expand

(a x^{2} + b x + c)^{2}

a^{2} x^{4} + b^{2} x^{2} + 2 a x^{3} b + 2 a x^{2} c + 2 b c x + c^{2}

Solution steps

(a x^{2} + b x + c)^{2}

Apply exponent rule:

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

(a x^{2} + b x + c)^{2} = (a x^{2} + b x + c) (a x^{2} + b x + c)

= (a x^{2} + b x + c) (a x^{2} + b x + c)

Distribute parentheses

= a x^{2} a x^{2} + a x^{2} b x + a x^{2} c + b x a x^{2} + b x b x + b x c + c a x^{2} + c b x + cc

Simplify

a x^{2} a x^{2} + a x^{2} b x + a x^{2} c + b x a x^{2} + b x b x + b x c + c a x^{2} + c b x + cc : a^{2} x^{4} + b^{2} x^{2} + 2 a x^{3} b + 2 a x^{2} c + 2 b c x + c^{2}

= a^{2} x^{4} + b^{2} x^{2} + 2 a x^{3} b + 2 a x^{2} c + 2 b c x + c^{2}

(x + a)^{3} (x + b)^{5}

\frac{9}{16} + (- \frac{11}{64})

\frac{4}{1} + \frac{1}{4}

14 (- 2 i + 6)

(2 x^{2} - 5 x - 3) + (- 10 x^{2} + 2 x + 7)

What is expand (ax^2+bx+c)^2 ?
The solution to expand (ax^2+bx+c)^2 is a^2x^4+b^2x^2+2ax^3b+2ax^2c+2bcx+c^2