What is expand (1+a+b)^3 ?

The solution to expand (1+a+b)^3 is a^3+b^3+3a^2+3a^2b+3a+6ab+3b^2+3b+3ab^2+1

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expand (1+a+b)^3

expand

(1 + a + b)^{3}

a^{3} + b^{3} + 3 a^{2} + 3 a^{2} b + 3 a + 6 ab + 3 b^{2} + 3 b + 3 a b^{2} + 1

Solution steps

(1 + a + b)^{3}

Simplify

(1 + a + b)^{3} : (1 + a + b) (1 + a + b) (1 + a + b)

= (1 + a + b) (1 + a + b) (1 + a + b)

Expand

(1 + a + b) (1 + a + b) : a^{2} + 2 a + 2 b + 2 ab + b^{2} + 1

= (a^{2} + 2 a + 2 b + 2 ab + b^{2} + 1) (1 + a + b)

Distribute parentheses

= a^{2} \cdot 1 + a^{2} a + a^{2} b + 2 a \cdot 1 + 2 aa + 2 ab + 2 b \cdot 1 + 2 ba + 2 bb + 2 ab \cdot 1 + 2 aba + 2 abb + b^{2} \cdot 1 + b^{2} a + b^{2} b + 1 \cdot 1 + 1 \cdot a + 1 \cdot b

Simplify

a^{2} \cdot 1 + a^{2} a + a^{2} b + 2 a \cdot 1 + 2 aa + 2 ab + 2 b \cdot 1 + 2 ba + 2 bb + 2 ab \cdot 1 + 2 aba + 2 abb + b^{2} \cdot 1 + b^{2} a + b^{2} b + 1 \cdot 1 + 1 \cdot a + 1 \cdot b : a^{3} + b^{3} + 3 a^{2} + 3 a^{2} b + 3 a + 6 ab + 3 b^{2} + 3 b + 3 a b^{2} + 1

= a^{3} + b^{3} + 3 a^{2} + 3 a^{2} b + 3 a + 6 ab + 3 b^{2} + 3 b + 3 a b^{2} + 1

\frac{( - 4 x ^{3} y ^{4} ) ^{- 2}}{( 6 x ^{2} y ^{5} ) ^{- 2}}

\frac{( w ^{2} + 2 w )}{w}

(3 y + 7)^{2}

(4 x + 3)^{3} - 125

y^{5} - 5 y^{3} + 3 y^{2} + 5 y + \frac{3}{100} y^{2} + 4 y + 2

What is expand (1+a+b)^3 ?
The solution to expand (1+a+b)^3 is a^3+b^3+3a^2+3a^2b+3a+6ab+3b^2+3b+3ab^2+1