Question

find the following product using appropriate identies
1.)(x+5)(x+5)
2.)(p-3)(p+3)
3.)(-1)(-1)
4.)(t+2)(t+4)
5.)102×98

Answer 1

1) (a+b)2
Ans- x2+10x+25
2) (a+b)(a-b)=a2-b2
Ans- p2-9
3) Ans-1
4)This is simple multiplication. No identity.
Ans- t2+6t+8
5) (a+b)(a-b)=a2-b2
(100+2)(100-2)
Ans- 9,996

Answer 2

1) (x+5) (x+5) = (x+5 )²
= x²+2*x*5+5²          [ (a+b)² ≡ a²+2ab+b²]
=x²+10x+25
2)(p-3)(p+3)
= p²-3²             [ (a+b)(a-b) ≡ a² - b² ]
=p²-9

3)(-1) (-1) = (-1) ² = 1

4) (t+2) (t+4)
= t² + (2+4)t + 2*4            [ (x+a) (x+b) ≡x²+(a+b) x+ab ]
=t² +6t+8
5)102  x 98
= (100+2) (100-2)    [(a+b)(a-b) ≡ a² -b²]
= 100² -2²
=10000-4
=9996