What is expand (3a^2(b-a)^2)/2 ?

The solution to expand (3a^2(b-a)^2)/2 is (3a^2b^2)/2-3a^3b+(3a^4)/2

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expand (3a^2(b-a)^2)/2

expand

\frac{3 a ^{2} ( b - a ) ^{2}}{2}

\frac{3 a ^{2} b ^{2}}{2} - 3 a^{3} b + \frac{3 a ^{4}}{2}

Solution steps

\frac{3 a ^{2} ( b - a ) ^{2}}{2}

(b - a)^{2} = b^{2} - 2 ab + a^{2}

= \frac{3 a ^{2} ( a ^{2} - 2 ab + b ^{2} )}{2}

Expand

3 a^{2} (b^{2} - 2 ba + a^{2}) : 3 a^{2} b^{2} - 6 a^{3} b + 3 a^{4}

= \frac{3 a ^{2} b ^{2} - 6 a ^{3} b + 3 a ^{4}}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{3 a ^{2} b ^{2} - 6 a ^{3} b + 3 a ^{4}}{2} = \frac{3 a ^{2} b ^{2}}{2} - \frac{6 a ^{3} b}{2} + \frac{3 a ^{4}}{2}

= \frac{3 a ^{2} b ^{2}}{2} - \frac{6 a ^{3} b}{2} + \frac{3 a ^{4}}{2}

Divide the numbers:

\frac{6}{2} = 3

= \frac{3 a ^{2} b ^{2}}{2} - 3 a^{3} b + \frac{3 a ^{4}}{2}

2 (x + 2 - 2 ln (x + 2))

\frac{2 x + 1}{( x - 2 ) ^{2}}

(e^{2 y} - 1) \cdot (e^{2 x} + 1)

\frac{2 x ^{2} - 8 x + 5}{( x - 2 ) ^{2}}

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

What is expand (3a^2(b-a)^2)/2 ?
The solution to expand (3a^2(b-a)^2)/2 is (3a^2b^2)/2-3a^3b+(3a^4)/2