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Popular >

simplify (a+b)^4-(a-b)^4

Solution

simplify

(a + b)^{4} - (a - b)^{4}

Solution

8 a^{3} b + 8 a b^{3}

Solution steps

(a + b)^{4} - (a - b)^{4}

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

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

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

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

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

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

Simplify

a^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3} + b^{4} - a^{4} + 4 a^{3} b - 6 a^{2} b^{2} + 4 a b^{3} - b^{4} : 8 a^{3} b + 8 a b^{3}

= 8 a^{3} b + 8 a b^{3}

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Frequently Asked Questions (FAQ)

What is (a+b)^4-(a-b)^4 ?
The solution to (a+b)^4-(a-b)^4 is 8a^3b+8ab^3