simplify by combining like terms: 1. (5x 3 – 3x) + (8x 3 + 4x) = 2. (4y 3 + 8xy) – (3xy + 9y 3...
TRANSCRIPT
Simplify by combining like terms:
1. (5x3 – 3x) + (8x3 + 4x) =
2. (4y3 + 8xy) – (3xy + 9y3)=
3. (5x3 – 2y3) – (5y3 + 6x3)=
13x3 + x
-5y3 + 5xy
-x3 – 7y3
1. 4x2 + 8x + 212. -7x2 + 17x – 233. 6x3 + 4x + 14. 7x3 + 8x2 + 3x – 135. 13x2 + 8x + 176. -2x2 + 11x + 187. -6x3 + x2 – x – 7 8. 8x3 – 2x2 + 159. 9x2 – 4x + 6310. 11x3 + 24x + 1
11. 2x2 + 2x – 412. -12x9 + 8x6 – 313. 7x3 – 16x + 1914. -x8 – 67x + 815. -16x2 + 34x – 9716. -6x2 – 29x + 1917. -22x3 – 13x2 + x18. -x6 – 34x4 + 2619. 8x2 – 15x + 6520. 2x + 1
21. 5xy2 + 11x – 8y2 22. 3x2 + 65xy + 5y2 – 9x23. 2.2x2 + .26xy – 13.7y2 24. 4x3 – 4x2 + 8x – 4
Distributive Property – Review!!!
3(x + 5) = 3x + 15
We will need that same concept to multiply polynomials.
3(2x2 + 4x + 3)= 6x2
We will distribute the outside term to everything on the inside.
+ 12x
+ 9
4(3x2 – 2x + 1) = 12x2 – 8x + 4
2x(2x2 + x + 5) = 4x3 + 2x2 + 10x
4 ∙ 3x2
4 ∙ –2x
4 ∙ 1
2x ∙ 2x2
2x ∙ x
2x ∙ 5
12x2 –8x +
4
4x3 +2x2
+10x
3x2 (2x3 + 2x2 – 2x)
= 6x5 + 6x4 – 6x3
3x2 ∙ 2x3
3x2 ∙ 2x2
3x2 ∙ – 2x
Notice the negative!
(2x + 2)(3x + 1)This gets a little more complicated! We
now have to distribute TWO terms!
Distributing this gets confusing!!!!
(2x + 2)(3x + 1)
I will show you two ways to multiply this: Expansion Boxes and FOIL.You decide which works for you!(I like Expansion Boxes!)
(2x + 2)(3x + 1)
Mult. 3x +1
2x
+2
Break each expression into terms.
(2x + 2)(3x + 1)Mult. 3x +1
2x
+2
Now we multiply!
6x2
(2x + 2)(3x + 1)Mult. 3x +1
2x
+2
Now we multiply!
6x2 + 2x
(2x + 2)(3x + 1)Mult. 3x +1
2x
+2
Now we multiply!
6x2 + 2x
+ 6x
(2x + 2)(3x + 1)Mult. 3x +1
2x
+2
Now we multiply!
6x2 + 2x
+ 6x
+ 2
(2x + 2)(3x + 1)Mult. 3x +1
2x
+2
Now we combine terms!
6x2 + 2x
+ 6x
+ 2
6x2 + 2x + 6x + 2 6x2 + 8x + 2
(2x + 1)(3x – 5)
6x2 – 10x + 3x – 5 6x2 – 7x – 5
Mult. +3x – 5
+2x
+ 1
+6x2 – 10x
+ 3x – 5
(x + 5)(-x – 2)
-x2 – 2x – 5x – 10 -x2 – 7x – 10
Mult. -x – 2
x
+ 5
-x2 – 2x
– 5x – 10
FOIL is an acronym for:
(2x + 2)(3x + 1)
FirstOuterInnerLast First: +2x ∙ +3x =
+6x2
FOIL is an acronym for:
(2x + 2)(3x + 1)
FirstOuterInnerLast First: +2x ∙ +3x =
+6x2 Outer: +2x ∙ +1 =
+2x
FOIL is an acronym for:
(2x + 2)(3x + 1)
FirstOuterInnerLast First: +2x ∙ +3x =
+6x2 Outer: +2x ∙ +1 =
+2xInner: +2 ∙ +3x = +6x
FOIL is an acronym for:
(2x + 2)(3x + 1)
FirstOuterInnerLast First: +2x ∙ +3x =
+6x2 Outer: +2x ∙ +1 =
+2xInner: +2 ∙ +3x = +6xLast: +2 ∙ +1 = +2
FOIL is an acronym for:
(2x + 2)(3x + 1)
FirstOuterInnerLast
First: +2x ∙ +3x = +6x2
Outer: +2x ∙ +1 = +2x
Inner: +2 ∙ +3x = +6xLast: +2 ∙ +1 = +2
Now we combine!6x2 + 2x + 6x + 2
6x2 + 8x + 2
(3x + 4)(5x – 2)
First: +3x ∙ +5x = +15x2
(3x + 4)(5x – 2)
First: +3x ∙ +5x = +15x2 Outer: +3x ∙ - 2 = - 6x
(3x + 4)(5x – 2)
First: +3x ∙ +5x = +15x2 Outer: +3x ∙ - 2 = - 6xInner: +4 ∙ +5x = +20x
(3x + 4)(5x – 2)
First: +3x ∙ +5x = +15x2 Outer: +3x ∙ - 2 = - 6xInner: +4 ∙ +5x = +20xLast: +4 ∙ - 2 = - 8
(3x + 4)(5x + 2)First: +3x ∙ +5x =
+15x2 Outer: +3x ∙ - 2 = -
6xInner: +4 ∙ +5x = +20xLast: +4 ∙ - 2 = - 8
Combine:15x2 – 6x + 20x – 8
15x2 + 14x – 8
(2x + 1)(4x – 3)
Combine:8x2 – 6x + 4x – 3
8x2 – 2x – 3
Mult. 4x – 3
2x
+ 1
8x2 – 6x
+ 4x
– 3
First: +2x ∙ +4x = +8x2
Outer: +2x ∙ -3 = -6xInner: +1 ∙ +4x = +4xLast: +1 ∙ -3 = -3Combine:
8x2 – 6x + 4x – 3 8x2 – 2x – 3
Same Answer!Same Answer!