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

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

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=5×5 (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 🙂

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