Advertisements
Advertisements
Question
Show that (m – n)2 + (m + n)2 = 2(m2 + n2)
Advertisements
Solution
Taking the L.H.S = (m – n)2 + (m + n)2
= m2 – 2mn + n2 + m2 + 2mn + n2
= m2 + n2 + m2 + n2
= 2m2 + 2n2 ...`[∵ {:(("a" + "b")^2 - 4"ab" = "a"^2 + 2"ab" + "b"^2),(("a" - "b")^2 = "a"^2 - 2"ab" + "b"^2)]`
= 2(m2 + n2)
= R.H.S
∴ (m – n)2 + (m + n)2 = 2(m2 + n2)
APPEARS IN
RELATED QUESTIONS
Expand (7m − 4)2
Factorise the following expressions
y2 – 10y + 25
Using suitable identities, evaluate the following.
(9.9)2
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.
4a2 – 4ab + b2
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
`x^2/4 - 2x + 4`
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
`9y^2 - 4xy + (4x^2)/9`
Factorise the following.
a2 – 16p – 80
If `x - 1/x = 7` then find the value of `x^2 + 1/x^2`.
