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Core Connections Integrated II, 2015 View details

1. Section 3.1

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Exercise 56 Page 172

Practice makes perfect

a To simplify the expression, we have to expand the parentheses. To do this, all terms in the first set of parentheses has to be multiplied by all terms in the second set of parentheses.

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

MultPar

Multiply parentheses

3 x* 4x -3x* 5+2* 4x - 2* 5

Multiply

12 x^2 - 15 x + 8 x - 10

AddTerms

Add terms

12 x^2 - 7x - 10

b Here, we will use the rules for expanding a squared binomial to simplify the expression.

(4 x - 1)^2

ExpandNegPerfectSquare

(a-b)^2=a^2-2ab+b^2

(4x)^2-2 * 4x * 1+1^2

PowProdII

(a b)^m=a^m b^m

4^2x^2-2 * 4x * 1+1^2

CalcPow

Calculate power

16x^2-2 * 4x * 1+1

Multiply

16x^2-8x+1

c To solve the equation, we first have to simplify the two sides as far as possible. After that, we can isolate x on one of the equation's sides by performing inverse operations.

2 x (x + 3 ) = (x + 1) (2 x - 5)

▼

Solve for x

Distr

Distribute 2x

2x* x + 2x * 3 = (x + 1) (2 x - 5)

MultPar

Multiply parentheses

2x* x + 2x * 3 = x* 2x-x* 5+1* 2x-1* 5

Multiply

2x^2 + 6x = 2x^2-5x+2x-5

AddTerms