Question

By using identities, find ( 5 x - 4 y)^2 + ( 5x + 4 y )^2​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Here , identity used :

(a+b)²=a²+b²+2ab

(a+b)²=a²+b²+2ab(a-b)²=a²+b²-2ab

Solving both terms separately:

(5x-4y)²

Here,it is in the form of (a-b)² where ,a=5x & b=4y

By using identity expanding the term :

=>(5x-4y)²= (5x)²+(4y)²-2(5x)(4y)

=>(5x-4y)²= 25x²+16y²-40xy

(5x+4y)²

Here,it is in the form of (a+b)² where ,a= 5x & b=4y

By using Identity expanding the term:

=>(5x+4y)²=(5x)²+(4y)²+2(5x)(4y)

=>(5x+4y)²=25x²+16y²+40xy

Now ,adding both term together

=>(5x-4y)²+(5x+4y)²

=>25x²+16y²-40xy+25x²+16y²+40xy

Making like terms together:

=>25x²+25x²+16y²+16y²-40xy+40xy

=>50x²+32y²

=>2(25x²+16y²) (answer)

Other Identities

$\bold{\boxed{ {x}^{3} + {y}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}}$

$\bold{\boxed{(x + y)(x + z) = {x}^{2} + (y+ z)x + yz}}$

$\bold{\boxed{ {(x +y)}^{3} = {x}^{3} + {y}^{3} +3xy[x+y]}}$

$\bold{\boxed{(x + a)(x - b) = {x}^{2} + (a - b)x - ab}}$

$\bold{\boxed{(x - a)(x - b) = {x}^{2} - (a + b)x + ab}}$

Answer 2

Answer:

(5x+2y)2+(5x−2y)2

=25x2+4y2+20xy+25x2+4y2−20xy

=50x2+8y2