1. Polynomial Multiplication: Square of a Binomial
4.5 Multiplication of Polynomials
5/21/2018
Polynomial Multiplication: Square of a Binomial
Square
of a
Binomial 2 + - = 2 2 2 + - +
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Kathy Monaghan & Pat Peterson - AIM

2. SQUARE
In mathematics, the SQUARE of a quantity (or expression) is the result of multiplying the quantity by itself.
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3. SQUARE: An Example Using Area
92 is read “nine squared” 92 = 9(9) = 81 which is the area of a square having side 9 units.
9 units
Area: 81 square units
9 units
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4. What happens when we Square a Binomial?F O I L
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5. Shortcut to Square (a+b)
Binomial Squared
square the first term
plus twice the product of the terms
plus the square of the second term
double
square
square
Perfect Square Trinomial
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6. Shortcut to Square (a-b)
Binomial Squared
square the first term
minus twice the product of the terms
plus the square of the second term
double
square
square
Perfect Square Trinomial
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7. Summary of the Shortcuts
Binomial Squared
Perfect Square Trinomial
Binomial Squared
Perfect Square Trinomial
A Shorter Way to Write the Rules:
Study these patterns carefully. They will be very useful when factoring trinomials in an advanced section.
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8. Squaring A Binomial: Shortcut Example 1
Binomial Squared
double
square
square
Perfect Square Trinomial
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9. Squaring A Binomial: Shortcut Example 2
Binomial Squared
double
square
square
Perfect Square Trinomial
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10. Squaring A Binomial: Shortcut Example 3
Binomial Squared
double
square
square
Perfect Square Trinomial
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11. Squaring A Binomial: Shortcut Example 4
Binomial Squared
double
square
square
Perfect Square Trinomial
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12. Squaring A Binomial: Shortcut Example 5
Binomial Squared
double
square
square
Perfect Square Trinomial
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13. Squaring A Binomial: Shortcut Example 6
Binomial Squared
double
square
square
Perfect Square Trinomial
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14. Memorize these Patterns for now and for later!
In a future section, we will need to work this problem in reverse. We will be given a perfect trinomial square and will need to rewrite it as a binomial squared.
Here’s are two examples.
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15. That’s All for Now!
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