Question

Use the Binomial Theorem to expand each binomial (5x-4y)^3

Answer 1

You should know that:

(a+b)(a+b)(a+b)

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

=a(a²+2ab+b²)+b(a²+2ab+b²)

=a³+2a²b+ab²+a²b+2ab²+b³

=a³+3a²b+3ab²+b³

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If a=5x and b=-4y

(5x+(-4y))³

=(5x-4y)³

=(5x)³+3(5x)²(-4y)+3(5x)(-4y)²+(-4y)³

=125x³+3(25x²)(-4y)+15x(16y²)-64y³

=125x³+75x²(-4y)+240xy²-64y³

=125x³-300x²y+240xy²-64y³