Question

f(x)=12(x²-y²),g(x)=8(x³-y³),show that f(x)*g(x)=LCM*GCD​

Answer 1

Step-by-step explanation:

f(x) = 12(x^2 - y^2)

g(x) = 8 ( x^3 - y^3 )

factors of ,

f(x) = 2×2×3 ×(x+y)(x-y)

g(x) = 2×2×2×(x+y)(x^2 - xy + y^2)

LCM = 2×2×3×(x+y)(x-y)(x^2- xy + y^2)

= 3×8(x-y) {(x+y)(x^2-xy+y^2)

=3(x-y) ×8(x^3-y^3)

= 3(x-y)× g(x)

HCF(GCD)= 2×2×(x+y)

= 4×(x+y)

now LCM×HCF

{3(x-y)×g(x)}×{4(x+y)}

3×4(x+ y)(x-y) ×g(x)

= 12(x^2 -y^2) × g(x)

= f(x) × g(X)

HP