In mathematics factorization is a process that is used to break down numbers into smaller numbers are discussed below.

The process of finding two or more expressions whose product is the given expression is called factorization.

**Note:**

Factorization is the reverse process of multiplication.

Follow the examples given below:

Product | Factorization |
---|---|

(i) 3x (4x - 5y) = 12x^{2} - 15xy |
12x^{2} – 15xy = 3x (4x - 5y) |

(ii) (x + 3)(x - 2) = x^{2} + x - 6 |
x^{2} + x - 6 = (x + 3)(x - 2) |

(iii) (2a + 3b)(2a – 3b) = 4a^{2} – 9b^{2} |
4a^{2} – 9b^{2} = (2a + 3b)(2a – 3b) |

Simple factorization:

Now we learn how to solve simple factorization.

We see that the HCF of both the terms is found. The HCF of the terms 36x

Each term of the given expression is multiplied and divided by the HCF.

\(3xy(\frac{36x^{2}y^{2}}{3xy} - \frac{15xy}{3xy})\)

= 3xy(12xy – 5)

The HCF of 15 and 12 = 3, common literal numbers are a, b and c. The lowest power of a = 3, b = 1 and c = 3.

Therefore, HCF of 15a

The HCF of 4, 14 and 2 = 2, common literal number is a. The lowest power of a = 1.

Therefore, HCF of 4a

**Remember: **

(i) HCF of two or more monomials = (HCF of their numerical coefficients) × (HCF of their literal coefficients)

(ii) HCF of literal coefficients = product of each common literal raised to the lowest power.

Some solved examples:

The HCF of the terms 8x

Therefore, 8x

The HCF of the terms 14m

Therefore, 14m

**3.** Factorize 5a(b
+ 3c) - 5m(b + 3c)

The HCF of the terms 5a(b + 3c) and 5m(b + 3c) = 5(b + 3c)

Therefore, 5a(b + 3c) - 5m(b + 3c) = 5(b + 3c) (a - m).

**Note:**

Thus, factorization is the method of expressing an algebraic expression as a product of two or more expressions.

**8th Grade Math Practice**

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