body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Core Connections: Course 3

CC

Core Connections: Course 3 View details

Chapter Closure

Exercise 121 Page 144

Remember, only like terms can be combined. Substitute - 1 and 6 for x and y, respectively, in the given expression. Be mindful of the negative sign before the parentheses when removing them.

Simplified Expression: x^2-5x-4-xy
Evaluated Expression: 8

We are given an expression and asked to simplify it and evaluate it for x=- 1 and y=6. We will do those things one at a time.

Simplifying

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. In this case, we have two x^2-terms, one x-term, one constant term, and two xy-terms. 3x^2 - 5x - 4 + xy-( 2xy + 2x^2) Only the x^2-terms and the xy-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. Since there is a negative sign before the parentheses, we will change the signs of all the terms inside when removing the parentheses.

3x^2-5x-4+xy-(2xy+2x^2)

Distribute - 1

3x^2-5x-4+xy-2xy-2x^2

CommutativePropAdd

Commutative Property of Addition

3x^2-2x^2-5x-4+xy-2xy

Subtract terms

x^2-5x-4-xy

Evaluating

To evaluate the simplified expression, we should substitute - 1 for x and 6 for y in the expression and then evaluate.

x^2-5x-4-xy

x= - 1, y= 6

( - 1)^2-5( - 1)-4-( - 1)( 6)

Calculate power

1-5(- 1)-4-(- 1)(6)

a(- b)=- a * b

1-(- 5)-4-(- 1)(6)

(- a)b = - ab

1-(- 5)-4-(- 6)

a-(- b)=a+b

1+5-4+6

Add and subtract terms

8

Subchapter links

Exercises