# Math Help - Expanding and Expanding brackets with FRACTIONAL POWERS

1. ## Expanding and Expanding brackets with FRACTIONAL POWERS

Hey guys,
bit stuck on how to expand+simply this equation. could you please help me out and post how to do get to the simplified equation?

the equation being:

Gamei

2. ## Re: Expanding and Expanding brackets with FRACTIONAL POWERS

You use the foil method as you would when multiplying polynomials of integer exponents. for a pair of binomials the foil method is (a+b)(c+d) = a(c+d) + b(c+d) = ac + ad + bc + bd (rearranging for like terms afterward)

so in this case we have
$(2x^\frac{1}{2}-3y^\frac{3}{2})(2x^\frac{1}{2} + 3y^\frac{3}{2})$
$(2x^\frac{1}{2})(2x^\frac{1}{2}) + (2x^\frac{1}{2})(3y^\frac{3}{2}) - (2x^\frac{1}{2})(3y^\frac{3}{2}) - (3y^\frac{3}{2})(3y^\frac{3}{2})$
$(2x^\frac{1}{2})(2x^\frac{1}{2}) - (3y^\frac{3}{2})(3y^\frac{3}{2})$
$4x - 9y^3$ by exponent rules. Recall $(a^b)(a^c) = a^{b+c}$

3. ## Re: Expanding and Expanding brackets with FRACTIONAL POWERS

Originally Posted by gamei
Hey guys,
bit stuck on how to expand+simply this equation. could you please help me out and post how to do get to the simplified equation?
the equation being:

Oh come on, the sum and difference of squares: $2x-9y^3$