Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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Squaring a Sum

To find (a + b)2, the square of a sum, we can use FOIL on (a + b)(a + b):

(a + b)(a + b) = a2 + ab + ab + b2
  = a2 + 2ab + b2

You can use the result a2 + 2ab + b2 that we obtained from FOIL to quickly find the square of any sum. To square a sum, we square the first term (a2), add twice the product of the two terms (2ab), then add the square of the last term (b2).


Rule for the Square of a Sum

(a + b)2 = a2 + 2ab + b2

In general, the square of a sum (a + b)is not equal to the sum of the squares a2 + b2. The square of a sum has the middle term 2ab.


Helpful hint

To visualize the square of a sum, draw a square with sides of length a + b as shown.

The area of the large square is (a + b)2. It comes from four terms as stated in the rule for the square of a sum.


Example 2

Squaring a sum

Square each sum, using the new rule.

a) (x + 5)2

b) (2w + 3)2

c) (2y4 + 3)2


a) (x + 5)2 = x2 + 2(x)(5) + 52 = x2 + 10x + 25

Square of first

Twice the product

Square of last


b) (2w + 3)2 = (2w)2 + 2(2w)(3) + 32 = 4w2 + 12w + 9

c) (2y4 + 3)2 = (2y4)2 + 2(2y4)(3) + 32 = 4y8 + 12y4 + 9


Squaring x + 5 correctly, as in Example 2(a), gives us the identity (x + 5)2 = x2 + 10x + 25, which is satisfied by any x. If you forget the middle term and write (x + 5)2 = x2 + 25, then you have an equation that is satisfied only if x = 0.

Helpful hint

You can use

(x + 5)2 = x2 + 10x + 25
  = x(x + 10) + 25

to learn a trick for squaring a number that ends in 5. For example, to find 252, find 20 · 30 + 25 or 625. More simply, to find 352, find 3 · 4 = 12 and follow that by 25: 352 = 1225.