How do you simplify -2x^2y^2(3x^2-xy+4y^2)2x2y2(3x2xy+4y2)?

1 Answer
Jun 26, 2015

Use distributivity and commutativity of multiplication to get:

-2x^2y^2(3x^2-xy+4y^2) = -6x^4y^2+2x^3y^3-8x^2y^42x2y2(3x2xy+4y2)=6x4y2+2x3y38x2y4

Explanation:

-2x^2y^2(3x^2-xy+4y^2)2x2y2(3x2xy+4y2)

=(-2x^2y^2*3x^2)+(-2x^2y^2*-xy)+(-2x^2y^2*4y^2)=(2x2y23x2)+(2x2y2xy)+(2x2y24y2)

= -6x^4y^2+2x^3y^3-8x^2y^4=6x4y2+2x3y38x2y4

Distributivity says that a(b+c) = ab+aca(b+c)=ab+ac or more generally:

a(b_1+b_2+...+b_n) = ab_1+ab_2+...+ab_n

Commutativity of multiplication says that:

a*b = b*a for any a and b.

Associativity of multiplication says that:

a*(b*c) = (a*b)*c for any a, b and c

More generally, we can miss out the brackets and not worry what order multiplication occurs in in a product like:

a_1*a_2*...*a_n

So for example -2x^2y^2*3x^2 = -2*3*x^2*x^2*y^2

Notice that when multiplying powers you add the exponents:

For example, x^2*x^2 = x^(2+2) = x^4