## Factoring Binomials - Difference of Squares

Algebra Games

Objective: I can factor binomials that are difference of squares.

A difference of squares is a binomial of the form:

a^{2}–b^{2}

Take note that the first term and the last term are both perfect squares.

When we factor a difference of two squares, we will get

a^{2}–b^{2}= (a + b)(a – b)

This is because (*a + b*)(*a – b*) = *a*^{2}– *ab* + *ab – b*^{2} = *a*^{2}– *b*^{2}

Read the lesson on Difference of Squares if you need more information.

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

**Factoring Binomials Calculator**

Type in the binomial and select factor.

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### Section 1-5 : Factoring Polynomials

For problems 1 – 4 factor out the greatest common factor from each polynomial.

- \(6{x^7} + 3{x^4} - 9{x^3}\) Solution
- \({a^3}{b^8} - 7{a^{10}}{b^4} + 2{a^5}{b^2}\) Solution
- \(2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5}\) Solution
- \({x^2}\left( {2 - 6x} \right) + 4x\left( {4 - 12x} \right)\) Solution

For problems 5 & 6 factor each of the following by grouping.

- \(7x + 7{x^3} + {x^4} + {x^6}\) Solution
- \(18x + 33 - 6{x^4} - 11{x^3}\) Solution

For problems 7 – 15 factor each of the following.

- \({x^2} - 2x - 8\) Solution
- \({z^2} - 10z + 21\) Solution
- \({y^2} + 16y + 60\) Solution
- \(5{x^2} + 14x - 3\) Solution
- \(6{t^2} - 19t - 7\) Solution
- \(4{z^2} + 19z + 12\) Solution
- \({x^2} + 14x + 49\) Solution
- \(4{w^2} - 25\) Solution
- \(81{x^2} - 36x + 4\) Solution

For problems 16 – 18 factor each of the following.

- \({x^6} + 3{x^3} - 4\) Solution
- \(3{z^5} - 17{z^4} - 28{z^3}\) Solution
- \(2{x^{14}} - 512{x^6}\) Solution

## Factoring practice

*x*^{2}+ 3 x - 10*x*^{2}*+ 2 x - 24**x*^{2}*- 9 x + 18**2 x*-^{2}*5 x - 12**x*^{2}*+ 4 x + 6**3 x*^{2}*+ 5 x + 2**x*^{2}+ 1.5 x - 10*x*^{2}*- x + 9**8 x*^{2}*- 62 x + 99**24 x*^{2}*- 22 x - 35**2x*^{3}*+ 3 x*^{2}*- 17 x - 30**x*^{3}*- 3 x*^{2}*- x + 3**x*^{3}*+ 4 x*^{2}*- 7 x + 2**18 x*^{3}*- 57 x*^{2}*- 85 x + 100*

### Answers

*(x - 2) (x + 5)**(x - 4) (x + 6)**(x - 3) (x - 6)**(x - 4) (2 x + 3)**It is as factored as it gets.**(3 x + 2) (x + 1)**(2 x + 5) (0.5 x - 2)**It is as factored as it gets.**(4 x - 9) (2 x - 11)**(4 x - 7) (6 x + 5)**(x - 3) (2 x + 5) (x + 2)**(x - 1) (x + 1) (x - 3)**(x - 1) (x*^{2}+ 5 x - 2) is as factored as it gets.*(x - 4) (3 x + 5) (6 x - 5)*

## Worksheet on Factoring Binomials

Practice the worksheet on factoring binomials to know how to find the common factor from the binomials. For factoring the binomials we need to find the common factor in each term so that we can find out the common factor.

**Note:** To practice factoring binomials recall the reverse method of distributive law means in short nu-distributing the factor.

**1. Factorize the following binomials:**

(i) 3a + 21

(ii) 7m – 14

^{3}+ 3y

(iv) 20x + 5x

^{2}

(v) – 16x + 20x

^{3}

(vi) 5x

^{2}y + 15xy

^{2}

(vii) 9a

^{2}+ 5a

(viii) 19a – 57b

(ix) 25a

^{2}b

^{2}c

^{3}– 15ab

^{3}c

**2. Factor each of the following algebraic expression:**

(i) 13n + 39

(ii) 19y - 57z

(iii) 21xy + 49xyz

^{3}

(v) 12x

^{2}y – 42xyz

(vi) 27a

^{3}b

^{3}+ 36a

^{4}b

^{2}

Answers for the worksheet on factoring binomials are given below to check the exact answers of the simple factors.

**Answers:**

**1.** (i) 3(a + 7)

(ii) 7(m - 2)

(iii) y(y + 3)

(iv) 5x(4 + x)

(v) 4x(-4 + 5x^{2})

(vi) 5xy(x + y)

(vii) a(9a + 5)

(viii) 19(a – 3b)

(ix) 5ab^{2}c(5ac

^{2}– 3b)

**2.** (i) 13(n + 3)

(ii) 19(y - 3z)

(iii) 7xy(3 - 7z)

(iv) 4p(-4 + 5p^{2})

(v) 6xy(2x – 7z)

(vi) 9a

^{3}b

^{2}(3b + 4a)

**8th Grade Math Practice**

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## Factoring binomials practice

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Factoring Trinomials The Easy Fast Way.

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