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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

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Exercise 10 Page 174

Use the formula for the difference of two squares.

6 and -6

Practice makes perfect

We want to solve the given equation by factoring.

Applying the Difference of Two Squares

Do you notice that the expression on the left-hand side of the equation is a difference of two perfect squares? This can be factored using the difference of squares method. a^2 - b^2 ⇔ (a+b)(a-b) To do so, we first need to express each term as a perfect square.

Expression	x^2-36
Rewrite as Perfect Squares	x^2 - 6^2
Apply the Formula	(x+6)(x-6)

Solving the Equation

Finally, to solve the equation, we will use the Zero Product Property.

x^2-36=0

▼

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

Write as a power

x^2-6^2=0

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

(x+6)(x-6)=0

Use the Zero Product Property

lcx+6=0 & (I) x-6=0 & (II)

(I): LHS-6=RHS-6

lx=- 6 x-6=0

(II): LHS+6=RHS+6

lx_1=- 6 x_2=6

Subchapter links

Exercises p.174-177