How do I use Pascal's triangle to expand a binomial?

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How do I use Pascal's triangle to expand a binomial?

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Answer 1 · 2015-10-31T09:31:53

Rows of Pascal's triangle provide the coefficients to expand $(a+b)^n$ as follows...

Explanation:

To expand $(a+b)^n$ look at the row of Pascal's triangle that begins $1, n$ . This provides the coefficients.

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For example, $(a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4$ from the row $1, 4, 6, 4, 1$

How about $(2x-5)^4$ ?

Let $a = 2x$ and $b = -5$ .

Then:

$(2x-5)^4 = (a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4$

$=(2x)^4+4(2x)^3(-5)+6(2x)^2(-5)^2+4(2x)(-5)^3+(-5)^4$

$=16x^4+4(8x^3)(-5)+6(4x^2)(25)+4(2x)(-125)+(625)$

$=16x^4-160x^3+600x^2-1000x+625$

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How do I use Pascal's triangle to expand a binomial?

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