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.
1. Factorize 36x^{2}y^{2} – 15xyEach 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)
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:
1. Factorize 8x^{3} - 32x^{5}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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