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August 11, 2016 How do I multiply polynomials? Adding Polynomials Review Subtracting Polynomials Review Multiplying Polynomials Add the following polynomials: (9x2 - 7x + 15) + (-3x2 + 9x - 8) Step 1: Group all like terms together (9x2-3x2) +(-7x+9x) +(15-8) 6x2 + 2x +7 Step 2: Make sure the expression is standard form Add the following polynomials using column form: (4x2 + 3y2) + (-3x2 –xy + 2y2) (4x2+ 3y2) + (-3x2 - xy + 2y2) Line up your like terms 4x2 + 3y2 + -3x2 - xy + 2y2 X2 -xy + 5y2 Subtract the following polynomials: (9x2 - 7x + 15x3) - (-3x2 + 8x - 8x3) Step 1: Rewrite subtraction as adding the opposite. (9x2 - 7x + 15x3) + (+ 3x2 - 8x + 8x3) Step 2: Group the like terms. (9x2 + 3x2)+ (- 7x - 8x) + (15x3 + 8x3) 12x2-15x+23x3 23x3+12x2-15x Add the following polynomials using column form: (4x2 – 2xy + 12) - (-6x2 +5xy - 7y2) (4x2 - 2xy + 12) + (6x2 - 5xy + 7y2) Line up your like terms 4x2 - 2xy + 12 + 6x2 - 5xy + 7y2 10X2 -7xy + 7y2 + 12 Multiply a polynomial by a monomial. Multiply a polynomial by a polynomial. Consider the following expression: 3 (x+6) This expression is the sum of x and 6 multiplied by 3. 3(x + 6) (3 *x) +(3 *6) 3x + 18 To simplify this expression we can distribute the multiplication by 3 to each number in the sum. Multiply: 3xy(2x + y) This problem is just like the review problems except for a few more variables. To multiply we need to distribute the 3xy over the addition. 3xy(2x + y) = (3xy * 2x) + (3xy * y) = 6x2y + 3xy2 We can also multiply a polynomial and a monomial using a vertical format in the same way we would multiply two numbers. Multiply: 7x(2xy – 3x) 2xy – 3x x___7x 14x2y – 21x2 Align the terms vertically with the monomial under the polynomial. Now multiply each term in the polynomial by the monomial. We will distribute the first polynomial through the second polynomial. Multiply: (x + 2)(x – 5) (x + 2)(x – 5) O F (x + 2)(x – 5) I Multiply the First terms. Multiply the Outside terms. Multiply the Inside terms. Multiply the Last terms. L After you multiply, collect like terms. This pattern for multiplying polynomials is called FOIL. (x – 6)(2x + 1) x(2x)+ x(1) – (6)2x – 6(1) 2x2 + x – 12x – 6 2x2 – 11x – 6 2x2(3xy + 7x – 2y) 2x2(3xy) + 2x2(7x) + 2x2(–2y) 6x3y + 14x3 – 4x2y (x + 4)(x – 3) x(x) + x(–3) + 4(x) + 4(–3) x2 – 3x + 4x – 12 x2 + x – 12 (2y – 3x)(y – 2) 2y(y) + 2y(–2) + (–3x)(y) + (–3x)(–2) 2y2 – 4y – 3xy + 6x