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Sunday 19th of May
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Writing a Rational Expression in Lowest Terms
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The Square of a Binomial
Properties of Negative Exponents
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Simple Trinomials as Products of Binomials
Ratios and Proportions
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Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
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Order of Operations
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The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
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Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
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The Square of 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.

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