Multiplying Standard vs Box Method

Unit 7 Non-Calculator Study Review

Multiply Binomials

Using box method:

• Create number of rows and boxes to match # of terms per expression. (2x2 for two Binomials)

• Multiply and combine terms

Box method example

The box method works with different combinations of polynomials.

(image: 4 term polynomial multiplying a Trinomial!)

Multiple Choice

Which of the following is the correct box method set-up to solve $$\left(x+2\right)\left(x+3\right)=$$  ?

Multiple Choice

Write the expanded (general) form of the product (x+3)(x+6).

• x²+18x+9

• x²+9x+18

• x²+18x+18

Multiple Choice

Multiply binomials using box method (2x +1) (x - 3).

• 2x³ -4x +3

• 2x + 5x -3

• 2x² -5x -3

• 2x -6x + 2

Multiple Choice

Find the product:
(3x + 2)(2x + 4)

• 6x² + 16x + 8

• 5x² +11x + 6

• 5x² + 16x + 6

• 6x² + 11x + 8

Target: Add Polynomials

​Watch your signs!!!

Combine Like Terms.

Write your answers in Standard Form.​

​

Multiple Choice

Find the sum (2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x²+ 5x -7

• -2x² + 11x -4

Multiple Choice

Simplify (2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

Multiple Choice

Simplify (4x³ - 5x² + 3x) + (-2x³ - x² + 6x)

• 2x³ - 6x² - 9x

• 2x³ + 6x² + 9x

• -2x³ - 6x² + 9x

• 2x³ - 6x² + 9x

Subtracting Polynomials Example

Multiple Choice

Subtract these polynomials:

(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Multiple Choice

Subtract these polynomials:

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3

• -7n² - 8n + 3

• -6n² - 8n + 3

• -7n² - 4n + 3

Multiple Choice

Subtract these polynomials:

(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x

• 7x⁵ - 6x

• -5x³ + 2x² - 6x

• -5x⁵ - 6x

Multiple Choice

Multiply (x + 9)(x – 9)

• x² + 18

• x² + 81

• x² – 81

• x² – 18

Multiple Choice

Factor x² – 144 completely

• x(x – 144)

• (x + 12)(x + 12)

• (x + 12)(x – 12)

• (x + 72)(x – 72)

Multiple Choice

x² + 81

• Prime

• ( x - 9 ) ( x + 9 )

• ( x + 9 ) ( x + 9 )

• ( x - 9 ) ( x - 9 )

Factor 16h² - 9a²

Remember: a² - b² = ​(a + b)(a - b)

There terms (16h²​) and (9a²) are both perfect squares.

​

Therefore 16h² = (4h)² because the √​16=4 and √h² = h

AND 9a² = (3a)² because √​9=3 and √a²=a

SO​

We can ​factor 16h² - 9a² to (4h + 3a)(4h-3a)

Note: Check my work​

Multiple Choice

x² - 25

• ( x + 5 ) ( x - 5 ) 

• ( x - 5 ) ( x - 5 ) 

• ( x + 5 ) ( x + 5 ) 

• Prime

Multiple Choice

4x² - 25

• (2x + 5) (2x - 5)

• (2x - 5)²

• (2x + 5)²

• 2x + 5(2x - 5)

Factoring Trinomials using the box/area model

The Box Method/Area Model

• Place the first term in the first inside box (top left) and the last term in the last box (bottom right)

• Find the factors of c that add to b

• Place those factors with x's in the other two boxes. It doesn't matter which is which.

• Factor out the GCF in each row and each column.

• Now group the outside and you're done!

The Box Method/Area Model when a>1

• Place the first term in the first inside box (top left) and the last term in the last box (bottom right)

• Multiply the a and the c

• Find the factors of ac that add to b

• Place those factors with x's in the other two boxes. It doesn't matter which is which.

• Factor out the GCF in each row and each column

• Now group the outside and you're done!

Don't forget your signs!

The sign for the bottom row and right column always come from the first term in the row or column

Now you try some!

Multiple Choice

Find the expression that should replace D

• -5

• 5x

• -x

• -1

Multiple Choice

What expressions should replace C and E?

• C=2 and E=-1x

• C=2x and E=1x

• C=2x and E=-5x

• C=2x² and E=-5x

Fill in the Blanks

Factor completely $\ b^2+8b+7$  

do not use any spaces in your answer 

i.e. (p+r)(p-r) not ( p + r )(p -r) ect

Fill in the Blanks

Factor Completely $3p^2-2p-5$   

Do not use spaces in your answers

Fill in the Blanks

Factor completely $2k^2+22k+60$  

Don't forget to look for a GCF (if it has one it should in go in front of your factored answer) and do not use spaces in your answer i.e. GCF(p-r)(p+r)

Multiple Choice

What is the area of the shaded region?

• $$2x^2+21x+54$$

• $$x^2-8x+15$$

• $$x^2+29x+41$$

• $$x^2+13x+69$$