Advertisements
Advertisements
Question
Simplify: (a + b)2 – (a – b)2
Advertisements
Solution
Applying the identities
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)2 – (a – b)2 = a2 + 2ab + b2 – [a2 – 2ab + b2]
= a2 + 2ab + b2 – a2 + 2ab – b2
= a2(1 – 1) + ab(2 + 2) + b2(1 – 1)
= 0a2 + 4ab + 0b2 = 4ab
(a + b)2 – (a – b)2 = 4ab
APPEARS IN
RELATED QUESTIONS
Factors of 4 – m2 are
(a – 1)2 = a2 – 1
The factors of x2 – 6x + 9 are
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
x2 – 8x + 16
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
x2 – 10x + 25
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
p2y2 – 2py + 1
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
a2y2 – 2aby + b2
Factorise the following.
x2 – 17x + 60
Factorise the following.
p2 – 13p – 30
If `x - 1/x = 7` then find the value of `x^2 + 1/x^2`.
