Question

geometric proof of algebraic 8 identities class 9 chapter 2

Answer 1

Step-by-step explanation:

Let us prove here, few identities.

1.(x + y)2 = x2 + y2 + 2xy

L.H.S. = (x + y)2

L.H.S. = (x + y) (x + y)

By multiplying each term, we get,

L.H.S = x2 + xy + xy + y2

L.H.S. = x2 + 2xy + y2

L.H.S. = R.H.S.

2.(x – y)2 = x2 + y2 – 2xy

By taking L.H.S.,

(x – y)2 = (x – y) (x – y)

(x – y)2 = x2 – xy – xy + y2

(x – y)2 = x2 – 2xy + y2

L.H.S. = R.H.S. Hence, proved.

3.x*2– y*2 = (x + y) (x – y)

By taking R.H.S and multiplying each term.

(x + y) (x – y) = x2 – xy + xy – y2

(x + y) (x – y) = x2 – y2

Or

x2 – y2 = (x + y) (x – y)

L.H.S. = R.H.S. Hence proved.