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 + - + 4.6b S KM & PP Kathy Monaghan & Pat Peterson - AIM

SQUARE In mathematics, the SQUARE of a quantity (or expression) is the result of multiplying the quantity by itself. 4.6b S KM & PP

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 4.6b S KM & PP

What happens when we Square a Binomial? F O I L 4.6b S KM & PP

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 4.6b S KM & PP

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 4.6b S KM & PP

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. 4.6b S KM & PP

Squaring A Binomial: Shortcut Example 1 Binomial Squared double square square Perfect Square Trinomial 4.6b S KM & PP

Squaring A Binomial: Shortcut Example 2 Binomial Squared double square square Perfect Square Trinomial 4.6b S KM & PP

Squaring A Binomial: Shortcut Example 3 Binomial Squared double square square Perfect Square Trinomial 4.6b S KM & PP

Squaring A Binomial: Shortcut Example 4 Binomial Squared double square square Perfect Square Trinomial 4.6b S KM & PP

Squaring A Binomial: Shortcut Example 5 Binomial Squared double square square Perfect Square Trinomial 4.6b S KM & PP

Squaring A Binomial: Shortcut Example 6 Binomial Squared double square square Perfect Square Trinomial 4.6b S KM & PP

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. 4.6b S KM & PP

That’s All for Now! 4.6b S KM & PP