Question

Factorize the following by using suitable identities:
(a) x2 - 6x + 9
(b) p2 - 18p +81
(c) m4 + 2mn2 + n4
(d) a6+ 8a3+ 16​

Answer 1

Answer:

1.1     Factoring  p2-18p+81  

The first term is,  p2  its coefficient is  1 .

The middle term is,  -18p  its coefficient is  -18 .

The last term, "the constant", is  +81  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 81 = 81  

Step-2 : Find two factors of  81  whose sum equals the coefficient of the middle term, which is   -18 .

    -81    +    -1    =    -82  

    -27    +    -3    =    -30  

    -9    +    -9    =    -18    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -9  

                   p2 - 9p - 9p - 81

Step-4 : Add up the first 2 terms, pulling out like factors :

                  p • (p-9)

            Add up the last 2 terms, pulling out common factors :

                  9 • (p-9)

Step-5 : Add up the four terms of step 4 :

                  (p-9)  •  (p-9)

           Which is the desired factorization

Step-by-step explanation:

Brainliest answer mark plz

Step-by-step explanation: