Question

What is the product? (x square root 7 - 3 square root 8) (x square root 7 - 3 square root 8)

Answer 1

`7x^2-12x√(14)+72`

Explanation:

First we write the product

(x square root 7 - 3 square root 8) (x square root 7 - 3 square root 8)

This is:

`(x√(7)-3√(8))(x√(7)-3√(8))`

Now apply the distributive property as shown below.

`(x√(7)-3√(8))(x√(7)-3√(8))=x√(7)*x√(7) -3√(8)*x√(7)-3√(8)*x√(7) +3√(8)*3√(8)`

`(x√(7)-3√(8))(x√(7)-3√(8))=(x√(7))^2 -6x√(7)*√(8)+9*(√(8))^2\\\\\\(x√(7)-3√(8))(x√(7)-3√(8))=7x^2 -12x√(7*2)+9*8\\\\(x√(7)-3√(8))(x√(7)-3√(8))=7x^2-12x√(14)+72`

Answer 2

The product is
`7x^2-12x√(14)+72`

Explanation:

We need to find product of:

`(x√(7)-3√(8) )(x√(7)-3√(8))`

We need to multiply these terms

`=x√(7)(x√(7)-3√(8))-3√(8)(x√(7)-3√(8))\\=x^2(√(7))^2-3x(√(7)*√(8))-3x(√(8)*√(7))+9(√(8))^2\\=x^2(7)-6x(√(7)*√(8))+9(8)\\=7x^2-6x√(56)+72 \\√(56)=2√(14)\\=7x^2-6x*2√(14)+72\\=7x^2-12x√(14)+72`

So, the product is
`7x^2-12x√(14)+72`