Question

How do you use the distributive property to rewrite it in factored form \[2x - 10x?\]

Answer 1

Hint: In this question we have simplified the given algebraic form. Next, we use the distributive property and then simplify to arrive at our final answer. Next, we rearrange the terms .And also we are going to multiply and subtraction in complete step by step solution.
The distributive property of multiplication states that\[a{\text{ }}\left( {{\text{ }}b{\text{ }} + {\text{ }}c{\text{ }}} \right){\text{ }} = {\text{ }}a{\text{ }}b{\text{ }} + {\text{ }}a{\text{ }}c\]. It's often used for equations when the terms within the parentheses can't be simplified because they contain one or more variables.

Complete step-by-step solution:
Given:
\[ \Rightarrow 2x - 10x\]
If you use the distributive property to factor, the common factor is divided out of the bracket.
We get,
\[ \Rightarrow 2x(1 - 5)\]
Next, we subtract the parenthesis in the above term and we get
\[ \Rightarrow 2x \times ( - 4)\]
Finally, multiply the above term and we get the required answer
\[ \Rightarrow - 8x\]

-8x is the required answer for a given algebraic equation.

Note: We have to mind that, “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
The distributive property tells us how to solve expressions in the form of\[a\left( {b + c} \right)\]. The distributive property is sometimes called the distributive law of multiplication and division. Then we need to remember to multiply first, before doing the addition.
Rule of distributive property:
The law relating the operations of multiplication and addition, stated symbolically\[a\left( {b{\text{ }} + {\text{ }}c} \right){\text{ }} = {\text{ }}ab{\text{ }} + {\text{ }}ac\]; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor\[b{\text{ }} + {\text{ }}c\], resulting in the product \[ab{\text{ }} + {\text{ }}ac.\]
There is another little hard way to find the answer.
Given:
\[ \Rightarrow 2x - 10x\]
First, we take the common number in the above term and we get
\[ \Rightarrow 2\left( {x - 5x} \right)\]
Next, we take variable $x$in the parenthesis and we get
\[ \Rightarrow 2x\left( {1 - 5} \right)\]
Next, we subtract the parenthesis in the above term and we get
\[ \Rightarrow 2x \times ( - 4)\]
Finally, multiply the above term and we get the required answer
\[ \Rightarrow - 8x\]
This is a required answer for a given algebraic equation.