Exercise 33 Page 394

We want to simplify following expression. 5(3x+4y) - 6(2x+5y) Recall that an algebraic expression is in simplest form if it has no like terms and no parentheses. Since the given expression contains like terms and parentheses, we can simplify it. To do this, let's multiply 5 by (3x+4y) and - 6 by (2x+5y) using the Distributive Property. Then we will group like terms using the Commutative Property of Addition.

5(3x+4y) - 6(2x+5y)

DiffToSum

a-b = a+(- b)

5(3x+4y) +[- 6(2x+5y)]

Distr

Distribute 5

5(3x) + 5(4y) +[- 6(2x+5y)]

Distr

Distribute - 6

5(3x) + 5(4y) +[(- 6)(2x)+(- 6)(5y)]

RemovePar

Remove parentheses

5(3x) + 5(4y) +(- 6)(2x)+(- 6)(5y)

Multiply

Multiply

15x+20y+(- 12x)+(- 30y)

CommutativePropAdd

Commutative Property of Addition

15x+(- 12x)+(- 30y) +20y

Now we can combine like terms using the Distributive Property. 15 x+( - 12 x) + ( - 30 y)+ 20 y [0.3em] = [0.3em] [ 15+( - 12)] x + ( - 30+ 20) y Finally, we will perform the addition and simplify the expression.

[15+(- 12)]x+(- 30+20)y

AddTerms

Add terms

3x+(- 10y)

AddNeg

a+(- b)=a-b

3x-10y

The expression written in simplest form is 3x-10y.