Advertisements
Advertisements
Question
Show that (m – n)2 + (m + n)2 = 2(m2 + n2)
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: (98)2
Expand the following square, using suitable identities
(b – 7)2
Expand the following square, using suitable identities
(xyz – 1)2
(a – b)2 + ______ = a2 – b2
1032 – 1022 = ______ × (103 – 102) = ______.
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.
4y2 – 12y + 9
Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.
`9y^2 - 4xy + (4x^2)/9`
Factorise the following.
y2 + 4y – 21
If x – y = 13 and xy = 28, then find x2 + y2.
