Question

12) using formula find the product of the
following:(1) (x-1) (x4 +x2 +1) (2) (2x+3y) (4x2-6xy+9y2)
​

Answer 1

Answer:

(1) (x^2-1) (x^4 +x^2 +1)

Using the algebraic identity

a^3-b^3=(a-b) (a^2+ab+b^2)

in this case, a = x^2 and b = 1

[(x^2)^3-1^3] = (x^2-1) [(x^2)^2+(x^2)(1)+1^2]

(x^6-1) = (x^2-1) (x^4 +x^2 +1)

hence it is verified that (x^6-1) is the solution to the given question

(2) (2x+3y) (4x^2-6xy+9y^2)

Using the algebraic identity

a^3+b^3=(a+b) (a^2-ab+b^2)

in this case, a = 2x and b = 3y

(2x^3+3y^3)=(2x+3y) [(2x)^2-(2x)(3y+(3y)^2]

= (2x+3y) (4x^2-6xy+9y^2)

hence it is verified that (2x^3+3y^3) is the solution to the given question