Multiplying Binomials

(a + b)(c + d)=ac + ad + bc + bd

To multiply binomials, you need to distribute twice. Notice in the pattern above that first the a was distributed to everything in the 2nd parenthesis (c and d). Then, the b was distributed to everything in the 2nd parenthesis (c and d).

One way to remember this is with the acronym FOIL
F: First - Multiply the first term in each parenthesis (a times c)
O: Outer - Multiply the outside terms (a times d)
I: Inner - Multiply the inner terms (b times c)
L: Last - Multiply the last term in each parenthesis (b times d)


Examples:

1) (x+5)(x + 2) = x2 + 2x + 5x + 10 = x2 + 7x + 10

First, we distribute the x (x + 2) and get x2+2x. (Or, if you're thinking of FOIL, we do the first and outer.)

Next, we distribute the 5 (x + 2)and get 5x+10. (Or, if you're thinking of FOIL, we do the inner and last.)

Now we have x2 + 2x + 5x + 10, but we are not finished because there is a set of like terms that we can add together. Add 2x and 5x to get 7x. Make sure the final answer is in standard form: x2+7x+10.


2) (2y + 6)(y - 4) = 2y2 - 8y + 6y - 24 = 2y2 - 2y - 24

First, we distribute the 2y (y - 4) and get 2y2 - 8y. (Or, if you're thinking of FOIL, we do the first and outer.)

Next, we distribute the 6 (y - 4)and get 6y - 24. (Or, if you're thinking of FOIL, we do the inner and last.)

Now we have 2y2 - 8y + 6y - 24, but we are not finished because there is a set of like terms that we can add together. Add -8y and 6y to get -2y. Make sure the final answer is in standard form: 2y2-2y - 24.


Practice:

1) (y + 3)(y + 8)
2) (x - 4)(x + 2)
3) (y2 + 9)(y + 7)
4) (a - 3)(a - 10)
5) (x2 - 2x)(x + 4)


Answers: 1) y2 + 11y + 24 2) x2 - 2x - 8 3) y3 + 7y2 + 9y + 63 4) a2 - 13a + 30 5) x3 + 2x2 - 8x

Related Links:
Math
Algebra
Factors
Polynomials
Algebra Topics
Classifying Polynomials
Writing Polynomials in Standard Form
Simplifying Polynomials
Adding Polynomials
Subtracting Polynomials
Multiplying monomials
Distributive Property (Multiplying a monomial by a polynomial)
Multiplying trinomials and polynomials
Dividing monomials
Dividing polynomials by monomials
Dividing polynomials by binomials
Factoring Polynomials: Common Factors
Factoring Polynomials: The difference of two squares


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