Question

Multiply the algebraic expressions using the FOIL method and simplify.

$\left(x+3y\right)\left(2x-y\right)$

Short answer

The solution$\left(x+3y\right)\left(2x-y\right)=2x^2+5xy-3y^2$

Step-by-step solution

Step 1. Apply the concept of multiplying algebraic expressions (FOIL).

To find the product of polynomials or other algebraic expressions, we need to use the Distributive Property repeatedly. In particular, using it three times on the product of two binomials, we multiply the two factors by multiplying each term in one factor by each term in the other factor and adding these products.

The acronym FOIL helps us remember that the product of two binomials is the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms.

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

Step 2. Multiply using FOIL method.

Given$\left(x+3y\right)\left(2x-y\right)$

$\left(x+3y\right)\left(2x-y\right)=x\cdot 2x+x\cdot (-y)+3y\cdot 2x+3y\cdot (-y)$

Step 3. Simplify.

Simplify the expression in Step 2:

$\begin{array}{l}\left(x+3y\right)\left(2x-y\right)=x\cdot 2x+x\cdot (-y)+3y\cdot 2x+3y\cdot (-y)\\ \Rightarrow \left(x+3y\right)\left(2x-y\right)=2x^2-xy+6xy-3y^2\\ \Rightarrow \left(x+3y\right)\left(2x-y\right)=2x^2+5xy-3y^2\end{array}$