Question

Using distributive property, find the product of (x+3)(x^2-2x+4)

Answer 1

We multiply each monomial of the first parenthesis by each monomial of the second parenthesis:

`(x+3)(x^2-2x+4)\\\\=(x)(x^2)+(x)(-2x)+(x)(4)+(3)(x^2)+(3)(-2x)+(3)(4)`

Use
`a^n\cdot a^m=a^(n+m)`

`=x^3-2x^2+4x+3x^2-6x+12`

combine like terms

`=x^3+(-2x^2+3x^2)+(4x-6x)+12=x^3+x^2-2x+12`

Answer 2

The distributive property says that the following is true:

`a(b + c) = ab + ac`

In our problem, we will consider the term outside (or
`a` in the first equation) to be
`(x + 3)` and we will consider the expression inside the parentheses to be
`(x^2 - 2x + 4)`. To use the distributive property, we are going to apply the outside term to all terms within the second expression. This is represented as:

`(x + 3)(x^2) - (x + 3)(2x) + (x + 3)(4)`

We can now use the distributive property again to simplify the new expression:

`(x + 3)(x^2 - 2x + 4) = x^3 + 3x^2 - 2x^2 - 6x + 4x + 12 = x^3 + x^2 - 2x + 12`

The answer is x³ + x² - 2x + 12.