Chapter Closure
Sign In
search
Exercise 124 Page 424
Use the Distributive Property.
Start by removing the parentheses.
When simplifying the expression, remember that only like terms can be combined.
A constant is a number with a known, fixed value.
x^2+7x+2
18x+5
3x^2+3x+8
4x+6
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.
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 and the same exponent — can be combined.
4x + 2 + 2x + x^2 + x
In this case, we have three x-terms, one x^2-term, 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.
4x+2+2x+x^2+x
CommutativePropAdd
Commutative Property of Addition
x^2+4x+2x+x+2
FactorOut
Factor out x
x^2+x(4+2+1)+2
AddTerms
Add terms
x^2+x(7)+2
Multiply
Multiply
x^2+7x+2
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.
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 and the same exponent — can be combined.
10x + 4 - 3 + 8x + 4
In this case, we have two x-terms and three constant terms. Both the x-terms and constant terms can be combined. Let's simplify the expression by rearranging it according to the Commutative Property of Addition and then combining like terms.
10x+4-3+8x+4
CommutativePropAdd
Commutative Property of Addition
10x+8x+4-3+4
FactorOut
Factor out x
x(10+8)+4-3+4
AddTerms
Add terms
x(18)+5
Multiply
Multiply
18x+5
The first 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 and the same exponent — can be combined.
4 + x^2 + 3x + 2x^2 + 4
In this case, we have one x-term, two x^2-terms, and two constant terms. Both the x^2-terms and constant terms can be combined. Let's simplify the expression by rearranging it according to the Commutative Property of Addition and then combining like terms.
4+x^2+3x+2x^2+4
CommutativePropAdd
Commutative Property of Addition
x^2+2x^2+3x+4+4
FactorOut
Factor out x^2
x^2(1+2)+3x+4+4
AddTerms
Add terms
x^2(3)+3x+8
Multiply
Multiply
3x^2+3x+8
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.
x+4+(x-1)+3+2x ⇕ x+4+x-1+3+2x
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.
x + 4 + x - 1 + 3 + 2x
In this case, we have three x-terms and three constant terms. Both the x-terms and constant terms can be combined. Let's simplify the expression by rearranging it according to the Commutative Property of Addition and then combining like terms.
x+4+x-1+3+2x
CommutativePropAdd
Commutative Property of Addition
x+x+2x+4-1+3
FactorOut
Factor out x
x(1+1+2)+4-1+3
AddTerms
Add terms
x(4)+6
Multiply
Multiply
4x+6
Loading content