Exercise 4 Page &nbsp; 234

Distribute (-1)

21x+(-1)(-16) + (-1)7x

(- a)(- b)=a* b

21x+16 + (-1)7x

MultNegPos

(- a)b = - ab

21x+16-7x

The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. 21x+ 16 - 7x In this case, we have two x-terms and one constant. Only the x-terms can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.

21x+16-7x

Commutative Property of Addition

21x-7x+16

SubTerm

Subtract term

14x+16

Before we try to simplify the given expression, let's use the |Distributive Property so that we can get rid of the parentheses. This will also let us see the correct coefficients for any terms with variables.

(-13n)-(17-5n)

Distribute (-1)

-13n+(-1)17+(-1)(-5n)

MultNegPos

(- a)b = - ab

-13n-17+(-1)(-5n)

(- a)(- b)=a* b

-13n-17+5n

The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. -13n - 17+ 5n In this case, we have two n-terms and one constant. Only the n-terms can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.

-13n-17+5n

Commutative Property of Addition

-13n+5n-17

SubTerm

Subtract term

-8n-17

(4y-7)-(y-7)

Distribute (-1)

4y-7+(-1)(y)+(-1)(-7)

MultNegPos

(- a)b = - ab

4y-7-y+(-1)(-7)

(- a)(- b)=a* b

4y-7-y+7

The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. 4y - 7 - y + 7 In this case, we have two y-terms and two constants. Both the y-terms and the constants can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.

4y-7-y+7

Commutative Property of Addition

4y-y-7+7

AddSubTerms

Add and subtract terms

(- w + 0.4)-(- w -0.4)

Distribute (-1)

- w + 0.4 +(-1)(- w) + (-1)(-0.4)

(- a)(- b)=a* b

- w + 0.4 + w + 0.4

The next step in simplifying this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. - w + 0.4 + w + 0.4 In this case, we have two w-terms and two constants. Both the w-terms and the constants can be combined, so to simplify the expression we will rearrange it according to the Commutative Property of Addition and then combine like terms.

- w + 0.4 + w + 0.4