# Multiply (x*y^2*z^3-v^4)(x*y^2*z^3+v^4) but do not use Foil method.

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We have to multiply (x*y^2*z^3-v^4) and (x*y^2*z^3+v^4)

We can see that the terms are of the form a - b and a + b with a=x*y^2*z^3 and b = v^4

We use the relation (a - b)(a + b) = a^2 - b^2

(x*y^2*z^3-v^4)*(x*y^2*z^3+v^4)

=> (x*y^2*z^3)^2 - (v^4)^2

=> x^2*y^4*z^6 - v^8

**The required product of the terms is x^2*y^4*z^6 - v^8**

We'll recognize the form (a-b)(a+b) and the product will become the difference of 2 squares.

(a-b)(a+b) = a^2 - b^2

a = x*y^2*z^3 and b = v^4

We'll raise to square a and b:

a^2 = (x*y^2*z^3)^2 = x^2*y^2*z^6

b^2 = (v^4)^2 = v^8

**Therefore, the result of multiplication, without using FOIL method, is: (x*y^2*z^3-v^4)(x*y^2*z^3+v^4) = x^2*y^4*z^6 - v^8.**