Question

factorise the following: 25m^2 + 30m + 9​

Answer 1

Given:

25m² + 30m + 9

solve the given question first we have to multiply 25 into 9

Here 25 × 9 = 225

And then check 225 factor of which number whose addition or subtraction equal to 30

So 15 × 15 is factor whose addition is 30

Here solve the equation are as follows:

25m² + 30m + 9

= 25m² + 15m + 15m + 9

=5m(5m + 3) + 3(5m + 3)

=(5m + 3)(5m + 3)

5m + 3=0  or  5m + 3=0

5m=-3  or 5m=-3

m=-3/5 or m=-3/5

Hence the factor of the given equation is m=-3/5 or m=-3/5

Answer 2

As per data given in the question,

We have to factorize the term - $25m^2+30m+9$

The given equation is in form of $ax^2+bx+c = 0$  

For solving the given question first we have to multiply (a) by (c) i.e. 25 by 9  So, we will get the product as - $25 \times 9=225$

Then we have to find the pair of numbers whose product is 225, and after doing addition and subtraction we can get 30/

So such numbers will be $15 \times 15$ whose addition is 30

So, the above equation can be simplified as,

$\begin{array}{l}25 m^{2}+30 m+9 \\=25 m^{2}+15 m+15 m+9 \\=5 m(5 m+3)+3(5 m+3) \\=(5 m+3)(5 m+3) \\5 m+3=0 \text { or } 5 m+3=0 \\5 m=-3 \text { or } 5 m=-3 \\m=-3 / 5 \text { or } m=-3 / 5\end{array}$

Hence the factor of the given equation will be $m=-3 / 5 \: and\:m=-3 / 5$