SOLUTION: Multiply. (2x � 5y)(3x � y)

Question 78810: Multiply. (2x � 5y)(3x � y)
Answer by mathdoc314(58) (Show Source): You can put this solution on YOUR website!

This involves variables but not substitution
This involves using variables and it involves using Distributive and Associative Laws of arithmetic and algebra
A * B + C * B = (A+C) * B Distributive Law
(A+B)+C = A + (B+C)
The other law is Commutative Law, A*B = B*A
The Commutative Law can be used to write the Distributive Law another way
A * B + A * C = A * (B + C)
In these laws A and B can be a number, a variable, or an expression.
Step 1: Distribute out the second factor
(2x � 5y)(3x � y) =
(2x - 5y)*(3x) + (2x - 5y) * (-y)
Step 2: Distribute out (2x - 5y) in both places
(2x)*(3x) - (5y)*(3x) + (2x)*(-y) + (-5y)(-y)
(You may have seen a shorter pattern for this:
(A+B)*(C+D) = A*C + A*D + B*C + B*D )
Step 3. Simplify those four terms
6x^2 - 15xy - 2xy + 5y^2
Step 4. Combine two like terms
6x^2 - 17xy + 5y^2
To learn this well, go back and look at the original expression, and the final answer, and see if you can grasp all those steps to understand how the transformation occurred.

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