multiplying polynomials. objective ncscos 1.01 b – write equivalent forms of algebraic expressions...
TRANSCRIPT
MULTIPLYING POLYNOMIALS
OBJECTIVE
• NCSCOS 1.01b – Write equivalent forms of algebraic expressions to solve problems.
•Operate with polynomials
•Students will know how to multiply polynomials by using the box method. They will use the rules of exponents and combining like terms to solve problems.
MULTIPLYING POLYNOMIALS
Binomial X Binomial
(3x + 2)(5x + 4)
BOX Method
)45)(23( xx
STEP 1: Draw the
BOX
BOX Method)45)(23( xx
2x2 for a Binomial x Binomial
BOX Method
)45)(23( xx
STEP 2: Place terms on outside
)45)(23( xx
x3 2x5
4
BOX Method
)45)(23( xx
STEP 3: MultiplyFind the area of
each box.
)45)(23( xx
x3 2x5
4
215x xx 35 25 x x10
x34 x12 24 8
BOX Method
)45)(23( xx
STEP 4: Combine Like Terms
x3 2x5
4
215x x10
x12 8
215x x22 8
BOX Method
)45)(23( xx
215x x22 8Why can’t I just combine like terms?
Because we’re multiplying, not adding!
BOX Method
LET’S SEE THAT
AGAIN!
BOX Method
STEP 1: Draw the
BOX
BOX Method
2x2 for a Binomial x Binomial
BOX Method
STEP 2: Place terms on outside
x5 3
BOX Method
STEP 3: MultiplyFind the area of
each box.
)56)(35( xx
x5 3230x xx 56 36 x x18
x55 x25 35 15
BOX Method
STEP 4: Combine Like Terms
)56)(35( xx
x5 3230x x18
x25 15
230x x7 15
BOX Method
230x x7 15
BOX Method
AND AGAIN!
BOX Method
STEP 1: Draw the
BOX
BOX Method
2x2 for a Binomial x Binomial
BOX Method
STEP 2: Place terms on outside
x4 7
BOX Method
STEP 3: MultiplyFind the area of
each box.
x4 728x xx 24 72 x x14
x49 x36 79 63
BOX Method
STEP 4: Combine Like Terms
x4 728x x14
x36 63
28x x50 63
BOX Method
28x x50 63
BOX Method
YOU TRY1.(5x – 1)(4x + 11)2.(2x – 3)(3x + 4)3.(2x2 + 3x)(4x2 – 2x)
BOX Method
2x2 for a Binomial x Binomial
)114)(15( xx
x5 1x4
11
)114)(15( xx
x5 1x4
11
220x x4
x55 11
)114)(15( xx
x5 1x4
11
220x x4
x55 11
220x x51 11
BOX Method
)114)(15( xx220x x51 11
BOX Method
What about a binomial x trinomial?
x4 338x 26x220x x15
x16 12
x4 322x
x5
4
38x 26x220x x15
x16 1238x 214x x 12
1.(x2 – 2x + 3)(2x + 4)2.(2x + 3)(4x2 – 2x + 4)3.(4x – 2)(5x2 – 4x – 3)
1.(x + 3)(x + 2)2.(2x + 4)(3x – 2)3.(-3x + 4)(5x – 6)4.(7x – 5)(5x – 7)5.(3x – 4)(3x2 – 2x – 4)