What is the rule for cubing a binomial?

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What is the rule for cubing a binomial?

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Answer 1 · 2015-10-26T23:00:29

${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ $(a+b)^3 = a^3+3a^2b+3ab^2+b^3$

Explanation:

The coefficients $1, 3, 3, 1$ $1, 3, 3, 1$ can be found as a row of Pascal's triangle:

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For other powers of a binomial use a different row of Pascal's triangle.

For example:

${(a + b)}^{5} = a^{5} + 5 a^{4} b + 10 a^{3} b^{2} + 10 a^{2} b^{3} + 5 a b^{4} + b^{5}$ $(a+b)^5 = a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$

How about ${(2 x - 5)}^{3}$ $(2x-5)^3$ or similar?

Let $a = 2 x$ $a=2x$ and $b = - 5$ $b=-5$ to find:

${(2 x - 5)}^{3}$ $(2x-5)^3$

$= {(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ $= (a+b)^3 = a^3+3a^2b+3ab^2+b^3$

$= {(2 x)}^{3} + 3 {(2 x)}^{2} (- 5) + 3 (2 x) {(- 5)}^{2} + {(- 5)}^{3}$ $=(2x)^3+3(2x)^2(-5)+3(2x)(-5)^2+(-5)^3$

$= 8 x^{3} - 60 x^{2} + 150 x - 125$ $=8x^3-60x^2+150x-125$

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What is the rule for cubing a binomial?

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