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Multiply Binomials
(ax + b)(cx +d)
(ax + by)(cx +dy)
- ( x - 9 ) ≤ 5
-1 -1
x - 9 ≥ -5
+9 +9
x ≥ 4
+ ( x - 9) ≤ 5
x - 9 ≤ 5
+9 +9
x ≤ 14
Neg.
Pos.
less than is an “and” statementless than is an “and” statement
What kind of statement?
Write as one inequality4 ≤ x and x ≤ 14≤ x and x ≤ 14
4 ≤ x ≤14 4 ≤ x ≤14 GraphGraph
Don’t forget To flipsymbol
| x - 9 | ≤ 5
Graph 4 ≤ x ≤14
<---|---|---|---|---|---|---|---|---|---> 2 4 6 8 10 12 14 16 18
Now shade
Between the
circles !!
What kind of
Circles?
6. A savings account is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. If an investment of $2,000 accumulate $360 of interest in the checking accounting after 4 years, what was the annual simple interest rate on the savings account?
I = PRT 360= 360 = (2,000)(4)R 360 = 8,000 R
8,000 8,000
0.045 = R
4.5% = R
Interest paid by bank Principle (invested) Rate is unknown Time is 4 years Regroup & Multiply Divide Change to %
(2,000) (R)(4)
FOIL or use Distributive Property
1. (3x + 4)(5x +1) Distribute the 3x Multiply (don’t
forget to add exponents when multiplying)
Distribute the 4 Like terms
add-same sign coefficients only (don’t add exp.)
3x20x 4
215 23 4x x
215x
FOIL or use Distributive Property
#2) (2x + 5)(3x +7) Distribute the 2x Multiply (don’t
forget to add exponents when multiplying)
Distribute the 5 Like terms
add-same sign coefficients only (don’t add exp.)
26x 14x15x 35
26 29 35x x
FOIL or use Distributive Property
#3) (4x + 5)(3x -8) Distribute the 4x Multiply (don’t
forget to add exponents when multiplying)
Distribute the 5 like terms
subtract- opposite signs coefficients only (don’t add exp.)
=12x2 - 32x
+15x - 40
=12x2 – 17x - 40
FOIL or use Distributive Property
#4) (3x - 2)(5x + 3) Distribute the 3x Multiply (don’t
forget to add exponents when multiplying)
Distribute the -2 like terms
subtract- opposite signs coefficients only (don’t add exp.)
=15x2
- 10x - 6
=15x2 – 1x - 6
+9x
FOIL or use Distributive Property
#5) (3x - 2)(2x - 7) Distribute the 3x Multiply (don’t
forget to add exponents when multiplying)
Distribute the -2 like terms
Add- same signs coefficients only (don’t add exp.)
=6x2 - 21x
- 4x + 14
=6x2 – 25x + 14
FOIL or use Distributive Property
#6) (4x - 8)(2x - 3) Distribute the 4x Multiply (don’t
forget to add exponents when multiplying)
Distribute the -8 like terms
Add- same signs coefficients only (don’t add exp.)
=8x2 - 12x
- 16x + 24
=8x2 – 28x + 24
FOIL or use Distributive Property
#7) (4x – 2y)(4x – 3y) Distribute the 4x Multiply (don’t
forget to add exponents when multiplying)
Distribute the -2y like terms add -
same signs coefficients only (don’t add exp.)
=16x2 - 12xy
- 8xy + 6y2
=16x2 – 20xy + 6y2
FOIL or use Distributive Property
#8) (2x + 9y)(3x + 2y) Distribute the 2x Multiply (don’t
forget to add exponents when multiplying)
Distribute the 9y Like terms
add-same sign coefficients only (don’t add exp.)
=6x2 + 4xy
+ 27xy + 18y2
=6x2 + 31xy + 18y2
FOIL or use Distributive Property
#9) (2x + 5y)(4x - 9y) Distribute the 2x Multiply (don’t
forget to add exponents when multiplying)
Distribute the 5y like terms
subtract- opposite signs coefficients only (don’t add exp.)
=8x2 - 18xy+ 20xy - 45y2
=8x2 + 2xy - 45y2
FOIL or use Distributive Property
10) (4x - 5y)(5x + 6y) Distribute the 4x Multiply (don’t
forget to add exponents when multiplying)
Distribute the -5y like terms
subtract- opposite signs coefficients only (don’t add exp.)
=20x2 + 24xy - 25xy - 30y2
=20x2 - xy - 30y2
(x-8)2 =
11) (x - 8)(x - 8) Distribute the x Multiply (don’t
forget to add exponents when multiplying)
Distribute the -8 like terms
Add- same signs coefficients only (don’t add exp.)
=x2- 8x
- 8x + 64
=x2 – 16x + 64
Write it twice!!!!!!!!
(x-8) (x-8)
(x+2)2 =
12) (x + 2)(x + 2) Distribute the x Multiply (don’t
forget to add exponents when multiplying)
Distribute the 2 like terms
Add- same signs coefficients only (don’t add exp.)
= x2 + 2x
+ 2x + 4
= x2 + 4x + 4
Write it twice!!!!!!!!
(x+2) (x+2)
(3x2+ ½ )2 =
(3x2+ ½ ) (3x2+ ½ ) Distribute the 3x2
Multiply (don’t forget to add exponents when multiplying)
Distribute the ½ like terms
Add- same signs coefficients only (don’t add exp.)
= 9x4
Write it twice!!!!!!!!
23
2x
23
2x
1
4
4 26 19
2 4x x
4 2 19 3
4x x
14) (2x2 – ¼ )2
(2x2 - ¼ ) (2x2 - ¼ ) Distribute the 2x2
Multiply (don’t forget to add exponents when multiplying)
Distribute the ¼ like terms
Add- same signs coefficients only (don’t add exp.)
= 4x4
Write it twice!!!!!!!!
22
4x
22
4x
1
16
4 24 14
4 16x x
4 2 14
16x x