Lesson 5; Factoring using special products

Lesson 5 (Intro activity)

Factoring using special products.

Do you remember the special products?

1. (a+b)² = a² + 2ab + b²
2. (a-b)² = a² - 2ab + b²
3. a²-b² = (a-b)(a+b) {a.k.a difference of squares}

Multiple Choice

Expand $$\left(a+b\right)^2$$  

• a²+b²

• a²+4ab+b²

• a²+2ab+b²

• 2a²+4ab+2b²

Multiple Choice

Expand $$\left(a-b\right)^2$$  

• a²-b²

• a²-4ab+b²

• a²-2ab+b²

• 2a²-4ab+2b²

Multiple Choice

Expand (a-b)(a+b)

• a²-b²

• a²+2ab+b²

• a²+b²

• a²-2ab+b²

Multiple Choice

Which of these is the expansion of (x+1)²

• x² + 2x + 1
• x² + x + 1
• 2x² + 2x + 1
• x² + x + 2

Multiple Choice

Which of these is the expansion of (x-1)²

• x² - 2x + 1

• x² + x + 1
• 2x² + 2x + 1
• x² + x + 2

Multiple Choice

Which of these is the expansion of (x+1)(x-1)

• x² - 1

• x² + 1

• 2x² + 1

• x² + 2

Multiple Choice

Which of these is the expansion of (x+2)²

• x² + 4x + 4
• x² + 2x + 4
• x² + 4x + 2
• 2x² + 4x + 4

Multiple Choice

Which of these is the expansion of (x-2)(x+2)

• x² - 4

• x² + 4

• 2x² - 4

• 2x² + 4

Multiple Choice

Which of these is the expansion of (x-2)(x+2)

• x² - 4

• x² + 4

• 2x² - 4

• 2x² + 4

Match

Match these special products with their correct expansions

• (x+5)²

• (x-7)²

• (2x+1)²

• (2x-3)²

• (x+9)²

x²+10x+25

x²-14x+49

4x²+4x+1

4x²-12x+9

x²+18x+81

• x²+10x+25

• x²-14x+49

• 4x²+4x+1

• 4x²-12x+9

• x²+18x+81

Dropdown

Write the missing terms in these special product expansions.

(x+1)² = x² + 2x + ​

Select answer

(x+2)² = x² + ​

Select answer

x + 4

(x+3)² = x² + 6x + ​

Select answer

(x-1)² = x² ​

Select answer

x + 1

(x-2)² = x² - 4x ​

Select answer

Drag and Drop

Write the missing term to complete these special product expansions;

x² + 12x + ​

Placeholder

(x-3)(x+​

Placeholder

)

x² + 8x + ​

Placeholder

x² + ​

Placeholder

x + 9

x² + 24x + ​

Placeholder

Drag these tiles and drop them in the correct blank above

36

3

16

6

144

Match

Match the following expansions to their missing terms;

• x²+ ___ + 64

• x² + ___ + 36

• x² - ___ + 49

• 4x²+ ___ + 25

• 9x² + ___ + 4

16x

12x

14x

20x

12x

• 16x

• 12x

• 14x

• 20x

• 12x

Factorizing using special products

We have seen how to expand using special products.
Example; (x+2)² = x²+4x+4

We can also reverse the process and factorize using special products.
Example; If we are given the expansion x²+4x+4

We can factorize it into (x+2)² {Kinda like the opposite}

Note; This only works for special products a.k.a perfect square trinomials.
Let's do some practice!

Multiple Choice

Is this an expansion of a special product?
x² + 16x + 64

• Yes
• No

Multiple Choice

Is this a perfect square trinomial?
x² + 16x + 64

• Yes
• No

Multiple Choice

Which of these is a perfect square trinomial?

• x² + 4x + 14

• x² + 2x + 1

• x² + 3x + 2

• x² + 5x + 6

Multiple Choice

Which if these is NOT a perfect square trinomial?

• x² + 6x + 9

• x² + 8x + 16

• x² + 10x + 25

• x² + 7x + 10

Multiple Choice

Factor the polynomial

$$k^2+14k+49$$  

• $$\left(k+7\right)^2$$

• $$\left(k-7\right)^2$$

• $$\left(k+7\right)\left(k-7\right)$$  

• $$\left(k+2\right)\left(k+7\right)$$  

Multiple Choice

Factor the polynomial

$$m^2-18m+81$$  

• $$\left(m+9\right)^2$$  

• $$\left(m-9\right)^2$$  

• $$\left(m+9\right)\left(m-9\right)$$  

• $$\left(m-1\right)\left(m-18\right)$$  

Multiple Choice

Factor.

x² + 24x + 144

• (x + 12)²

• (x - 12)²

• (x + 15)²

• (x + 13)²

Multiple Choice

Factor.

x² - 30x + 225

• (x + 15)²

• (x - 15)²

• (x + 25)²

• (x - 25)²

Multiple Choice

Factorize

x² + 24x + 144

• (x + 12)²

• (x - 12)²

Multiple Choice

Factorize;

x² - 30x + 225

• (x - 15)²

• (x + 15)²

Multiple Choice

Factor: x² + 24x + 144

• (x + 12)²
• (x + 9)²
• (x + 15)²
• (x + 13)²

Multiple Choice

Factor: x² - 4x + 4

• (x + 2)²
• (x - 2)²
• (x + 4)²
• (x - 4)²

Multiple Choice

Which of the following is a perfect square trinomial?

• x² – 4x – 4 
• x² – 6x – 9 
• x² + 6x – 9 
• x² – 4x + 4 

Multiple Choice

Factor completely: 25x²+60x+36

• (25x-6)(x-1)
• (5x-6)(5x-6)
• (5x+6)²
• (25x+4)(x+9)

Multiple Choice

Factor completely: 16x²-24x+9

• (16x-3)(x-3)
• (16x+9)(x+1)
• (4x-3)(4x-3)
• (4x+3)(4x+3)

Multiple Choice

Factor: 4x² - 20x + 25

• (4x - 25) (x -1)
• (2x + 5) (2x - 5)
• (2x - 5)²
• (4x - 5) (x - 5)

Multiple Choice

Factor

x² + 18x + 81

• (x + 9)(x – 9)

• (x + 9)²

• (x + 6)²

Multiple Choice

Factorize;

x² - 20x + 100

• (x-10)²
• (x+10)²

Multiple Choice

Factor: x² - 4x + 4

• (x + 2)²
• (x - 2)²
• (x - 4)²

Multiple Choice

Factor:
 n² + 10n + 25

• (n + 5)(n - 5)
• (n - 5)²
• (n + 5)²