Question

(a) Factorise the following expressions:-
(i) p2 + 8p + 16
(ii) 25a2 - 4​

Answer 1

Given:

two expressions:

(i) p²+8p+16

(ii)25a²-4

To find:

factors of the given expressions

Solution:

(i) p²+8p+16

split middle term

=p²+(4+4)p+16

use distributive law

=p²+4p+4p+16

take it common outside

=p(p+4)+4(p+4)

=(p+4)(p+4)

=(p+4)²

Hence, factor of p²+8p+16 is (p+4)²

(ii) 25a²-4

first, make a square

=(5a)²-2²

use algebraic identity a²-b²=(a+b)(a-b)

=(5a-2)(5a+2)

Hence, factor of 25a²-4 is (5a-2)(5a+2)