Question

(i) Write the expansion of (x + y)² and (x - y)². (ii) Find (x + y)² - (x - y)² (iii) Write 12 as the difference of two perfect square.

Answer 1

Step-by-step explanation:

(i) (x+y)^2 = x^2 + y^2 + 2xy

(x-y)^2 = x^2 + y^2 - 2xy

(ii) (x+y)^2 - (x-y)^2

= x^2 + y^2 + 2xy - (x^2 + y^2 - 2xy)

= x^2 + y^2 + 2xy - x^2- y^2 + 2xy

= 4xy

(iii) 4^2 - 2^2

i.e. 16-4

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Answer 2

Answer:

Step-by-step explanation:

1 ) We know the identity -

(x^2 - y^2) = ( x + y ) ( x - y )

The question is in the form of this identity where;

x = x + y

y = x - y

So based on the formulae the answer will be :

= ( x + y + x - y ) ( x + y - x - y )

For the first bracket x and x will add up to 2x and y and -y will get canceled

For the second bracket y and y will add up to 2y and x and -x will get canceled

So the answer is,

= (2x) (2y)

2 ) 12 as a sum of prime numbers

= 7 + 5 = 12

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