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How do you simplify $\left( 3x-1 \right)\left( 2x+6 \right)$ ?

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Last updated date: 19th Jul 2024
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Answer
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Hint: In this question, we have to simplify the given algebraic expression. Thus, we will use the distributive property and the basic mathematical rules to get the solution. As we know, the distributive property means opening the brackets of the given polynomials, such that every term is multiplied by each term. Thus, we will apply the distributive property $\left( a+b \right)\left( c+d \right)=a\left( c+d \right)+b\left( c+d \right)$ in the given expression. Then, we will again apply the distributive property $a\left( c+d \right)+b\left( c+d \right)=ac+ad+bc+bd$ in the new expression. After that, we will make the necessary calculations using the basic mathematical rules to get the required result for the solution.

Complete step by step solution:
According to the question, we have to simplify the given algebraic expression.
Thus, we will use the distributive property to get the solution.
The algebraic expression given to us is $\left( 3x-1 \right)\left( 2x+6 \right)$ -------- (1)
Now, we will first apply the distributive property $\left( a+b \right)\left( c+d \right)=a\left( c+d \right)+b\left( c+d \right)$ in expression (1), we get
$\Rightarrow 3x\left( 2x+6 \right)+\left( -1 \right)\left( 2x+6 \right)$
Now, we will again apply the distributive property $a\left( c+d \right)+b\left( c+d \right)=ac+ad+bc+bd$ in the above expression, we get
$\Rightarrow 3x\left( 2x \right)+3x\left( 6 \right)+\left( -1 \right)\left( 2x \right)+\left( -1 \right)\left( 6 \right)$
On opening the brackets of the above expression, we get
$\Rightarrow 6{{x}^{2}}+18x+\left( -2x \right)+\left( -6 \right)$
On further simplifying, we get
$\Rightarrow 6{{x}^{2}}+18x-2x-6$
In the above equation, x is common in two terms, thus we will solve them further, we get
$\Rightarrow 6{{x}^{2}}+16x-6$
Therefore, for the algebraic expression $\left( 3x-1 \right)\left( 2x+6 \right)$ , its simplified value is equal to $6{{x}^{2}}+16x-6$ .

Note:
While solving this problem, do mention the formulas you are using to avoid confusion and mathematical errors. One of the alternative methods to solve this problem is you can directly put the formula $\left( a+b \right)\left( c+d \right)=ac+ad+bc+bd$ in the given expression, to get the accurate answer to the problem.