What is a^2*(b+c)-(b+c)^3 ?

The solution to a^2*(b+c)-(b+c)^3 is a^2b+a^2c-b^3-3b^2c-3bc^2-c^3

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simplify a^2*(b+c)-(b+c)^3

simplify

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

a^{2} b + a^{2} c - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

Solution steps

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

(b + c)^{3} : b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3}

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

Expand

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

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

- (b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3}) : - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

= a^{2} b + a^{2} c - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

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

18 x^{2} + 39 x y - 15 y^{2}

\frac{( 4 a ^{4} - 8 a ^{2} \cdot b ^{2} + 4 b ^{4} )}{( a ^{2} \cdot b - b ^{3} )}

(3 + 8) \cdot x^{6} - 42 - 7

\frac{1}{( x )}

What is a^2*(b+c)-(b+c)^3 ?
The solution to a^2*(b+c)-(b+c)^3 is a^2b+a^2c-b^3-3b^2c-3bc^2-c^3