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Popular >

expand (x+a)^3(x+b)^5

Solution

expand

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

Solution

x^{8} + 5 x^{7} b + 10 x^{6} b^{2} + 10 x^{5} b^{3} + 5 x^{4} b^{4} + x^{3} b^{5} + 3 a x^{7} + 15 a x^{6} b + 30 a x^{5} b^{2} + 30 a x^{4} b^{3} + 15 a x^{3} b^{4} + 3 a x^{2} b^{5} + 3 x^{6} a^{2} + 15 x^{5} a^{2} b + 30 x^{4} a^{2} b^{2} + 30 x^{3} a^{2} b^{3} + 15 x^{2} a^{2} b^{4} + 3 x a^{2} b^{5} + a^{3} x^{5} + 5 a^{3} x^{4} b + 10 a^{3} b^{2} x^{3} + 10 a^{3} b^{3} x^{2} + 5 x a^{3} b^{4} + a^{3} b^{5}

Solution steps

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

Expand

(x + a)^{3} : x^{3} + 3 a x^{2} + 3 x a^{2} + a^{3}

= (x^{3} + 3 a x^{2} + 3 x a^{2} + a^{3}) (x + b)^{5}

= (x + b)^{5} (x^{3} + 3 a x^{2} + 3 x a^{2} + a^{3})

Distribute parentheses

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

= x^{3} (x + b)^{5} + 3 a x^{2} (x + b)^{5} + 3 x a^{2} (x + b)^{5} + a^{3} (x + b)^{5}

Expand

x^{3} (x + b)^{5} : x^{8} + 5 x^{7} b + 10 x^{6} b^{2} + 10 x^{5} b^{3} + 5 x^{4} b^{4} + x^{3} b^{5}

= x^{8} + 5 x^{7} b + 10 x^{6} b^{2} + 10 x^{5} b^{3} + 5 x^{4} b^{4} + x^{3} b^{5} + 3 a x^{2} (x + b)^{5} + 3 x a^{2} (x + b)^{5} + a^{3} (x + b)^{5}

Expand

3 a x^{2} (x + b)^{5} : 3 a x^{7} + 15 a x^{6} b + 30 a x^{5} b^{2} + 30 a x^{4} b^{3} + 15 a x^{3} b^{4} + 3 a x^{2} b^{5}

= x^{8} + 5 x^{7} b + 10 x^{6} b^{2} + 10 x^{5} b^{3} + 5 x^{4} b^{4} + x^{3} b^{5} + 3 a x^{7} + 15 a x^{6} b + 30 a x^{5} b^{2} + 30 a x^{4} b^{3} + 15 a x^{3} b^{4} + 3 a x^{2} b^{5} + 3 x a^{2} (x + b)^{5} + a^{3} (x + b)^{5}

Expand

3 x a^{2} (x + b)^{5} : 3 x^{6} a^{2} + 15 x^{5} a^{2} b + 30 x^{4} a^{2} b^{2} + 30 x^{3} a^{2} b^{3} + 15 x^{2} a^{2} b^{4} + 3 x a^{2} b^{5}

= x^{8} + 5 x^{7} b + 10 x^{6} b^{2} + 10 x^{5} b^{3} + 5 x^{4} b^{4} + x^{3} b^{5} + 3 a x^{7} + 15 a x^{6} b + 30 a x^{5} b^{2} + 30 a x^{4} b^{3} + 15 a x^{3} b^{4} + 3 a x^{2} b^{5} + 3 x^{6} a^{2} + 15 x^{5} a^{2} b + 30 x^{4} a^{2} b^{2} + 30 x^{3} a^{2} b^{3} + 15 x^{2} a^{2} b^{4} + 3 x a^{2} b^{5} + a^{3} (x + b)^{5}

Expand

a^{3} (x + b)^{5} : a^{3} x^{5} + 5 a^{3} x^{4} b + 10 a^{3} b^{2} x^{3} + 10 a^{3} b^{3} x^{2} + 5 x a^{3} b^{4} + a^{3} b^{5}

= x^{8} + 5 x^{7} b + 10 x^{6} b^{2} + 10 x^{5} b^{3} + 5 x^{4} b^{4} + x^{3} b^{5} + 3 a x^{7} + 15 a x^{6} b + 30 a x^{5} b^{2} + 30 a x^{4} b^{3} + 15 a x^{3} b^{4} + 3 a x^{2} b^{5} + 3 x^{6} a^{2} + 15 x^{5} a^{2} b + 30 x^{4} a^{2} b^{2} + 30 x^{3} a^{2} b^{3} + 15 x^{2} a^{2} b^{4} + 3 x a^{2} b^{5} + a^{3} x^{5} + 5 a^{3} x^{4} b + 10 a^{3} b^{2} x^{3} + 10 a^{3} b^{3} x^{2} + 5 x a^{3} b^{4} + a^{3} b^{5}

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Frequently Asked Questions (FAQ)

What is expand (x+a)^3(x+b)^5 ?
The solution to expand (x+a)^3(x+b)^5 is