Question

plz do this. factorize 6m^2n+9mn^2​

Answer 1

Answer:

=3mn (2m+3n)

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Given- }}$

$\sf \: Factorize \: : \: 6 {m}^{2}n + 9 {mn}^{2}$

$\large\underline{\sf{Solution-}}$

Concept Used :-

1. Method of Common Factors

• In this method of Common Factors, we have to express each term in the form of irreducible factors.

• Then find the common factors amongst all these irreducible factors.

• The required factorize form is the product of the common term we had taken out and the left over terms inside.

Let's solve the problem now!!

$\rm :\longmapsto\:\: 6 {m}^{2}n + 9 {mn}^{2}$

$\sf \: \: \: = \: \: \: 2 \times 3 \times m \times m \times n + 3 \times 3 \times n \times n \times m$

$\sf \: \: \: = \: \: \: 2 \times m \times \red{3 \times m \times n} + 3 \times n \times \red{ 3 \times n \times m}$

$\sf \: \: \: = \: \: \: \red{3 \times m \times n} \times (2 \times m + 3 \times n)$

$\sf \: \: \: = \: \: \: 3mn(2m + 3n)$

$\bf\implies \:\: 6 {m}^{2}n + 9 {mn}^{2} = 3mn(2m + 3n)$

Additional Information :-

Factorisation by Regrouping Terms

Sometimes it happens that there is no common term in the given expressions,

then

• We have to make the groups of the terms.

• Then choose the common factor among these groups.

• Find the common binomial factor and it will give the required factors.

For example,

$\rm :\longmapsto\:Factorize \: : \: ax + by + ay + bx$

$\sf \: \: \: = \: \: \: (ax + ay) + (bx + by)$

$\sf \: \: \: = \: \: \: a(x + y) + b(x + y)$

$\sf \: \: \: = \: \: \: (x + y)(a + b)$