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.