Please plesae answer these questions ita really urgent
Answers
Answer:
8) a) proved
8) d) proved
8) c) proved
Step-by-step explanation:
8)a)
(a+b) ^2 - (a-b) ^2
(a^2 +b^2 + 2ab) - (a^2 + b^2 - 2ab)
a^2 + b^2 + 2ab - a^2 - b^2 + 2ab
4ab (+ and - a^2 and b^2 gets cancelled)
8)d)
(a-b) ^2 = a^2 + b^2 - 2ab
(b-a) ^2 = b^2 + a^2 - 2ba
hence the two formulae are same this is also proved
8)c)
(5a^2 - 2b^2)^2 + 40a^2 b^2
25 a^4 + 4 b^4 + 20 a^2 b^2
(5a^2 + 2b^2)^2 [write in (a+b) ^2 formula]
Answer:
a)(a+b)²-(a-b)²=4ab
(a²+2ab+b²)-(a²-2ab+b²)=4ab
a²+2ab+b²-a²+2ab-b²=4ab
a²-a²+b²-b²+2ab+2ab=4ab
4ab=4ab
L.H.S.=R.H.S.
Hence proved
b)(x²+y²)(x²-y²)-(x²-y²)²=2(x²y²-y^4)
(x²)²-(y²)²-(x^4-2x²y²+y^4)=2(x²y²-y^4)
x^4-y^4-x^4+2x²y²-y^4=2(x²y²-y^4)
x^4-x^4+2x²y²-y^4-y^4=2(x²y²-y^4)
2x²y²-2y^4=2(x²y²-y^4)
2(x²y²-y^4)=2(x²y²-y^4)
L.H.S.=R.H.S.
Hence proved
c)(5a²-2b²)²+40a²b²=(5a²+2b²)²
25a^4-20a²b²+4b^4+40a²b²=(5a²+2b²)²
25a^4-20a²b²+40a²b²+4b^4=(5a²+2b²)²
25a^4+20a²b²+4b^4=(5a²+2b²)²
(5a²+2b²)²=(5a²+2b²)²
L.H.S.=R.H.S.
Hence proved
d)(a-b)²=(b-a)²
a²-2ab+b²=b²-2ab+a²
b²-2ab+a²=b²-2ab+a²
L.H.S.=R.H.S.
Hence proved