Question

factorise the following expression using appropriate identities 1) m²+10m+25 2) 49s²-36​

Answer 1

Step-by-step explanation:

Factorisation means writing a number or an expression as a product of its several factors which are smaller and simpler

So lets start the 1st question

1) m² +10m +25

to factorise this question we will use the product , sum, factor method which is

we look at the m²..what is its value ? its 1, the we look at the number having no m , its 25

so the product is 1×25 =25

the sum is the number associated to the m (not m²) which is 10

so now we need 2 factors , which when we multiplu becomes 25 and when we add both their sum is 10

lets neaten our datas

product=25

sum=10

factor=5x5 (why we too 5×5 and not 1×25 is because 5×5 is 25 and at the same time 5+5=10)

Now that we got our factor lets factorise our question

we simply have to write m + or - our factors depending if our factor is positive or negative and here our factors are both positive , so our answer is

(m+5)(m+5)

Now if we were asked to solve this question

we would equal (m+5)(m+5) by 0 and then solve

(m+5)(m+5)=0

then we would solve it like (m+5)=0 , m= -5

but this is a factoring exercise so we dont have to solve it.

2) 49s²-36

This specific type of question is based on this formula a² z b² = (a+b) (a–b )

so as we see , theres a minus present which applies to our formula ..theres also a s²

now theres 49 and 36

can we not make those as square numbers ? 49=7²and 36=6²

so lets apply this to our expression and factorise

49s²–36

7²s²–6²

(7s+6)(7s–6)

hope you understand and please pay attention to where it asks solving and where factoring

factoring is only a way to represent the expression in a much neater way which solving means finding the value of m or s or whatever the unknown might be :)