Question

Multiply the following expressions

$( {z}^{2} - 2 {y}^{2} + {x}^{2} )3 {x}^{2}( {y}^{2} - {x}^{2})$
​

Answer 1

Answer:

(3x+2y)

2

+(3x−2y)

2

Using identity:

(a+b)

2

=a

2

+b

2

+2ab

(a−b)

2

=a

2

+b

2

−2ab

Therefore,

(3x+2y)

2

+(3x−2y)

2

=[(3x)

2

+(2y)

2

+2(3x)(2y)]+[(3x)

2

+(2y)

2

−2(3x)(2y)]

=[9x

2

+4y

2

+12xy]+[9x

2

+4y

2

−12xy]

=9x

2

+4y

2

+12xy+9x

2

+4y

2

−12xy

=18x

2

+8y

2

=2(9x

2

+4y

2

)

Hence (3x+2y)

2

+(3x−2y)

2

=2(9x

2

+4y

2