Question

How do you use the distributive property to factor $2{{k}^{2}}+4k$ ?

Answer 1

Hint: In this question, we have to find the factors of a polynomial. Thus, we will use the distributive property to get the solution. As we know, the distributive property is in the form of $a\left( b+c \right)=ab+ac$, thus in this problem, we have to find the left-hand side of the formula, because the right hand side is given to us. So, first, we will find the factors of each term that are variable and the numbers. After that, we will take the common number and the variable from both the terms. In the last, we will put the uncommon terms in the bracket to get the required solution for the problem.

Complete step by step solution:
According to the question, we have to find the factors of the polynomial using the distributive property.
The polynomial given to us is $2{{k}^{2}}+4k$ ----------- (1)
Now, we will first find the factors of the numbers and the polynomial of the terms in equation (1), we get
$2=1\times 2$
${{k}^{2}}=1\times k\times k$
$4=1\times 2\times 2$
$k=1\times k$
So, now we will put these factors in equation (1), we get
$\Rightarrow \left( 1\times 2 \right)\left( 1\times k\times k \right)+\left( 2\times 2 \right)\left( 1\times k\times 1 \right)$
Now, we will take common 1, 2, and k from both the terms in the above equation, we get
$\Rightarrow \left( 1\times 2\times k \right)\left( k+2 \right)$
Thus, on further simplification, we get
$\Rightarrow 2k\left( k+2 \right)$ which is the required solution.
Therefore, for the polynomial $2{{k}^{2}}+4k$, its factors using the distributive property is equal to $2k\left( k+2 \right)$.

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical error. For checking your solution, apply the distributive property $a\left( b+c \right)=ab+ac$ in the solution to get the required problem. In this problem basically we take the common terms from the expression and the rest part comes in the bracket.