Question

How do you find the product of\[\left( x-7 \right)\left( x-6 \right)\]?

Answer 1

Hint: For the given problem, we are given to find a product. Since the equation contains an unknown variable ‘x’ we can’t do simple multiplication. So, for this we have to use the distributive property of multiplication. By using the property we can simply find the product of the given equation.

Complete step-by-step answer:
For the given problem we have to find the product of\[\left( x-7 \right)\left( x-6 \right)\].
Let us consider the given equation as equation (1).
\[q=\left( x-7 \right)\left( x-6 \right)..........\left( 1 \right)\]
By observing the equation we can see a variable ‘x’ in that. So we can’t subtract the terms \[\left( x-7 \right)\]and\[\left( x-6 \right)\]. That’s why we have to use the distributive property of multiplication.
Which states
“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.”
Now multiply \[x\] term and \[-7\] term with \[\left( x-6 \right)\]term individually and then add, we get
\[q={{x}^{2}}-6x+\left( -7x+42 \right)\]
By simplifying above equation we get
 \[\Rightarrow q={{x}^{2}}-6x-7x+42\]
Let us consider
\[q={{x}^{2}}-6x-7x+42........\left( 2 \right)\]
Taking -1 common from the terms -6x and -7x, we get
\[q={{x}^{2}}-\left( 6x+7x \right)+42\]
Now adding the term 6x+7x, we get
\[q={{x}^{2}}-13x+42\]
Let us consider
\[q={{x}^{2}}-13x+42.......\left( 3 \right)\]
So, therefore by the distributive property of multiplication the product of \[\left( x-7 \right)\left( x-6 \right)\] is\[{{x}^{2}}-13x+42\].

Note: Students must be aware of all properties like associative property, commutative property, closure property and distributive property because examiner may ask problems on any of these laws. Students should avoid calculation mistakes while doing multiplication in this problem because very minute mistakes may change the result of the problem.