Question

Using proper identities find the products of the following

I) (8x +3y)(8x – 7y)

II) (2a-5b)2​

Answer 1

Step-by-step explanation:

(8x+3y)(8x-7y)

a+b × a-b = a²-b²

so , 64x²-56y+24xy-21y²

Answer 2

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

We have two given term

(1) (8x+3y)(8x-7y)

(2) (2a-5b)²

Solving first part :

(1) (8x+3y) (8x-7y)

Here,the given term is in the form of (x+a)(x-b)

identity used here :

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

here , x= 8x ; a= 3y ; b= 7y

Put values into identity

=>(8x+3y)(8x-7y)= (8x)²+(3y-7y)x-(3y)(7y)

=>(8x+3y)(8x-7y)=64x²-4xy-21y²

solving second part

=>(2a-5b)²

Here ,it is in the form of (a-b)²

identity used here :

(a-b)²=a²+b²-2ab

=>(2a-5b)²= (2a)²+(5b)²-2(2a)(5b)

=>(2a-5b)²= 4a²+25b²-20ab

Other related identities:

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

$\bold{\boxed{ {(x -y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$

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

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

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