by: ellen moore emoore@clarendon3.org how to addingsubtracting multiplying a binomial by a binomial...

By: Ellen Moore

emoore@clarendon3.org

How to

Adding Subtracting

Multiplying a Binomial by a Binomial

Examples

Practice

How to

Examples

Practice

How to

Examples

Practice

ReferencesStandards

Adding Polynomials

You will combine like terms.

Remember like terms have exactly the same variable, variables, and exponents.

To add them you will add or subtract the coefficients. Whatever the signs say to do.

Remember the coefficients are the big numbers.

Examples of adding

1.( 3x2 -4x + 8) + (2x - 7x2 – 5)

=(3x2 – 7x2) + (-4x +2x) + (8-5)

= - 4x2 – 2x + 3

2.(3n2 – 8 +2n) + ( 5n + 13 + n2)

= ( 3n2 + 1n2) + ( 2n + 5n) + (-8 +13)

=4n2 + 7n + 5

Practice on Adding (2b3 -4b +b2) + ( -9b2 + 3b3 )

.

Wrong! Try again.

Wrong! Try again.

a. 11b3 -10b2 + 4b

b. 5b3 + 10b2 -4b

c. 5b3 -8b2 -4b

Subtracting Polynomials

Remember subtraction means to add the opposite.

To subtract polynomials you will add the opposite.

To add the opposite you will change the signs of every term in the second polynomial and then add.

Examples of Subtracting

1.(3n2 + 13n3 + 5n) – (7n + 4n3 )= (3n2 + 13n3 +5n) + (-7n – 4n3 )= ( 13n3 -4n3 ) + (3n2 ) + (5n-7n)= 9n3 +3n2 -2n

2. ( 6y2 + 8y4 -5y)-( 9y4 -7y +2y2 )= (6y2 +8y4 -5y) + (-9y4 +7y – 2y2 )= (8y4 -9y4 ) + (6y2 -2y2 ) + (-5y +7y)= -y4 + 4y2 + 2y

Practice on Subtracting

( -4y2 –y + 10) – ( 4y2 + 3y + 7)

a. 8y2 + 2y + 17

That’s correct!

b.-8y2 + 2y +3

c. -8y2 -4y+3

Multiplying two Binomials

To multiply two binomials you use the FOIL method.F- Multiply the first term in each binomial.O- Multiply the outside terms- first one in the first binomial and last one in the second.I- Multiply the inside terms which will be the last one in the first binomial and the first in the second one.L-Multiply the last term in each binomial.Then you will combine like terms if you have any. Usually the outsides and the insides yield like terms.

Examples of multiplying two binomials

( n+ 3) (n + 5) = Firsts (n x n)=n2

Outsides (n x 5)=5nInsides (3 x n)=3nLasts (3 x 5) = 15n2 + 5n + 3n + 15 – collect like terms= n2 + 8n + 15

Practice on Multiplying Two Binomials

1.( n + 6 ) ( n+ 2 )=

a. n2+ 6n + 2n + 8

c. 2n2 + 8n +12

b. n2 + 8n + 12

You got the correct answer.

Standards:

South Carolina State StandardsEA-2.7 Carry out a procedure ( including

addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions.

References:

Glencoe Mathematics Algebra 1. Glencoe McGraw-Hill.