Question

Describe the relationship between using the Distributive Property to simplify an expression and to factor an expression. Give an example to justify your answer.

Answer 1

Step 1: We know that

The distributive property is:

$x(y-z)=xy-xz$ and $x(y+z)=xy+xz$

It means you can separate the common term and represent it as the factor.

Step 2: The relationship between using the Distributive Property to simplify an expression and to factor an expression is given here.
The distributive property tells that $x(y-z)=xy-xz$ and $x(y+z)=xy+xz$

It means you can separate the common term and represent it as the factor.

Let us take one example question $12x+40y$
The factors of $12x=3\times 4\times x$ and the factors of $40y=5\times 2\times 4\times y$
The common factor is $4$. So, take out the common factor and use the Distributive property.
$$\begin{gathered} 12x+4y=4\left(3x\right)+4\left(10y\right) \\ =4(3x+10y) \end{gathered}$$