Question

Find the product using distributive law of multiplication: $\left( x-8 \right)\left( x-2 \right)$

Answer 1

Hint: Start by letting (x-8) to be t. On doing so, the expression becomes t(x-2), which when simplified using the distributive nature of multiplication, we get xt-2t. Now put the value of t and again simplify using the distributive nature of multiplication and solve the resulting expression to reach the answer.

Complete step-by-step answer:
Let us start the solution to the above question by letting (x-8) to be t. So, we can say that:
$x-8=t..........(i)$
Now if we substitute in the expression $\left( x-8 \right)\left( x-2 \right)$ , which is asked in the question. On doing so, we get
$t\left( x-2 \right)$
Now according to the distributive rule of multiplication $a\left( b\pm c \right)=ab\pm ac$ . So, if we use this in our expression, we get
$xt-2t$
Now we will substitute the value of t from equation (i). On doing so, we get
$x\left( x-8 \right)-2\left( x-8 \right)$
Again, if we use the distributive rule of multiplication, we get
 ${{x}^{2}}-8x-2x+16$
Now as there are two linear terms with variable x, we will add them. On doing so, we get
${{x}^{2}}-10x+16$
Hence, the answer to the above question is ${{x}^{2}}-10x+16$ .

Note:Remember that when you use the distributive rule of multiplication, not only the number but the signs of the numbers are also multiplies and it is generally seen that students makes a mistake in this part mostly, they generally take $-2\left( x-8 \right)=-2x-16$ , which is completely wrong. Also, if you notice that the final expression you get is a quadratic expression and its factors are (x-2) and (x-8), which are the terms in the original expression.