Question

How do you find the product ${{\left( 6x-1 \right)}^{2}}$ ?

Answer 1

Hint: The given problem can be easily done by multiplying $\left( 6x-1 \right)$ with itself. Then we use the foil method where we multiply each of the individual terms in the left parenthesis by each individual term in the right parenthesis. Further simplifying and adding the like terms we reach to the solution of the given product.

Complete step-by-step answer:
The expression we have is
${{\left( 6x-1 \right)}^{2}}$
If a term is squared or it has $2$ as its indices then it is basically the multiplication of the term with itself.
Therefore, we can rewrite the given expression as
$\left( 6x-1 \right)\left( 6x-1 \right)$
Now, we can apply the Foil method for multiplication. According to the Foil method if two terms are multiplied with each other then we should multiply each of the individual terms in the left parenthesis by each individual term in the right parenthesis.
Applying Foil method on the above expression we get
\[=(6x\times 6x)-(6x\times 1)-(1\times 6x)+(1\times 1)\]
Doing the multiplications of the above expression
\[=36{{x}^{2}}-6x-6x+1\]
We can now combine the like terms of the above expression and get
\[=36{{x}^{2}}-\left( 6+6 \right)x+1\]
Applying the distributive property in the middle term of the above expression as shown below
\[=36{{x}^{2}}-12x+1\]
Therefore, we conclude the result of the product ${{\left( 6x-1 \right)}^{2}}$ as \[36{{x}^{2}}-12x+1\] .

Note: While multiplying with the help of foil method we must be very careful about multiplying the terms, otherwise mistakes will occur. Also, we must keep in mind that the negative and positive signs are properly taken into account. The given expression can also be solved by using the formula of ${{\left( a-b \right)}^{2}}$ , where $a=6x$ and $b=1$ . We can substitute the above relations in the formula ${{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$ and get the same outcome as we have already got in our solution.