Page 561 - Algebra 1

Application: Garden Planning
Ganesh is designing a square border around a square pond. The area of the pond is 225 square feet. Use the difference of two squares to write an expression that represents the area of the border.
Example
4
546 Saxon Algebra 1
SOLUTION
Area of larger square:
A = lw
= (2f )(2f )
2f
border
Area of pond:
A = lw
225 = (15)(15)
pond
Math Reasoning
Analyze Suppose the side length of the larger square is double the side length of the pond. What is the area of the border?
Find the difference between the area of the square surrounding the pond and the area of the pond.
(2f )2 - (15)2 Write as a difference of two squares. = (2f - 15)(2f + 15) Factor.
The area of the border is (2f - 15)(2f + 15) ft2.
Determine whether the polynomial is a perfect-square trinomial. If so, factor the trinomial.
(Ex 1)
a. x2 +14x+49
b. 6n4 -12n2 +6
c. 3g2 +9g+9
d. A radio tower’s signal covers a circular area with a radius r in miles.
Lesson Practice
(Ex 2)
πr2 + 12πr + 36π square miles. By how much did the radius of the
The strength of the signal is increased, and now covers an area of coverage area increase?
Determine whether the binomial is the difference of two squares. If so, factor
the binomial.
(Ex 3)
e. 25x2 -4 f. 9b2 -100a2
g. x2 -14 h. -81+x10
i. A square border is designed around a square pool.
(Ex 4)
Use the difference of two squares to write and factor an expression that represents the area of the border.
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