Respuesta :
Factorization of 5m + 10m³ - 15m, is 10m(m - 1)(m + 1)
Given: To factorize 5m + 10m³ - 15m
What is factorization?
Factorization is the process of dividing a large value or algebraic equation or expression into smaller parts to simplify the problem. Multiplying all the smaller parts will give us the original problem.
We are given a problem say,
Example: Find for which values of x the value of the equation x² - 3x + 2 becomes 0. It will be difficult to guess the solutions for x by applying the hit and trial method or by guessing. If we factorize x² - 3x + 2 then we get (x - 1)(x - 2) and it becomes easy to find the solutions for which the value of the equation becomes 0 that is x = 1 and x = 2.
This process of representing or dividing x² - 3x + 2 in the form of the product of smaller quantities that is (x - 1)(x - 2) is known as factorization.
Why is factorization important?
Factorization helps us to break down a bigger problem into a form of products of multiple smaller problems which are easier to solve and also it gives a better idea for approaching a solution and hence saves time too. It places an important role in solving large equations.
Let's solve the given question.
To factorize: 5m + 10m³ - 15m
Grouping 5m and -15m, and then simplifying them
= 10m³ + (5m - 15m)
= 10m³ + (-10m)
= 10m³ - 10m [ ( + ) + ( - ) = ( - ) ]
Taking 10m common, we get
= 10m(m² - 1)
= 10m(m² - 1²) [1² = 1]
Expanding (m² - 1²)
= 10m(m - 1)(m + 1) [Formula : a² - b² = (a - b)(a + b)]
Therefore, 5m + 10m³ - 15m = 10m(m - 1)(m + 1)
Hence after factorization 5m + 10m³ - 15m is reduced to 10m(m - 1)(m + 1)
Know more about "factorization" here: https://brainly.com/question/18187355
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