Question

4p²-20p+25 factorise using (a-b) identity.​

Answer 1

Step-1 : Multiply the coefficient of the first term by the constant 4 • 25 = 100

Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .

-100 + -1 = -101

-50 + -2 = -52

-25 + -4 = -29

-20 + -5 = -25

-10 + -10 = -20 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10

4p2 - 10p - 10p - 25

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

2p • (2p-5)

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

5 • (2p-5)

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

(2p-5) • (2p-5)

Which is the desired factorization

Answer 2

$\large\fbox\red{Answer}$

$4 {p}^{2} - 20p + 25 \\ \\ = 4 {p}^{2} - (10 + 10)p + 25 \\ \\ = 4 {p}^{2} - 10p - 10p + 25 \\ \\ = 2p(2p - 5) - 5(2p - 5) \\ \\ = (2p - 5)(2p - 5)$

Thnku :)