Exercise 31 Page 393

We want to write the simplify following expression. 10(5g+2h-3)-4(3g-4h+2) 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 10 by (5g+2h-3) and - 4 by (3g-4h+2) using the Distributive Property. Then we will group like terms using the Commutative Property of Addition.

10(5g+2h-3)-4(3g-4h+2)

DiffToSum

a-b = a+(- b)

10(5g+2h-3)+[- 4(3g-4h+2)]

Distr

Distribute 10

10(5g)+10(2h)-10(3)+[- 4(3g-4h+2)]

Distr

Distribute - 4

10(5g)+10(2h)-10(3)+[(- 4)(3g)-(- 4)(4h)+(- 4)(2)]

Multiply

Multiply

50g+20h-30+[(- 12g)-(- 16h)+(- 8)]

SubNeg

a-(- b)=a+b

50g+20h-30+[(- 12g)+16h+(- 8)]

RemovePar

Remove parentheses

50g+20h-30+(- 12g)+16h+(- 8)

DiffToSum

a-b = a+(- b)

50g+20h+(- 30)+(- 12g)+16h+(- 8)

CommutativePropAdd

Commutative Property of Addition

50g+(- 12g)+20h+16h+(- 30)+(- 8)

AddTerms

Add terms

50g+(- 12g)+20h+16h+(- 38)

Now we can combine like terms using the Distributive Property. 50 g+( - 12 g) + 20 h+ 16 h+(- 38) [0.3em] = [0.3em] [ 50+( - 12)] g + ( 20+ 16) h +(- 38) Finally, we will perform the addition and simplify the expression.

[50+(- 12)]g+(20+16)h+(- 38)

AddNeg

a+(- b)=a-b

[50-12]g+(20+16)h - 38

AddSubTerms

Add and subtract terms

38g+36h-38

The expression written in simplest form is 38g+36h-38.