please so by multiplying binomials (x+6)(8x-x)
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Are you sure the second term in parentheses is 8x - x ? That is the same thing as 7x, which is not a binomial.
The binomial multiplication procedure you are probably supposed to be learning is often called by its abbreviation FOIL. You can read about it here:
http://www.algebrahelp.com/lessons/simplifying/foilmethod/
To multiply binomials (x + 6)(8x - x), you can use the distributive property. The distributive property states that for any three numbers a, b, and c: a(b + c) = ab + ac.
So, let's apply this rule to the given binomials:
(x + 6)(8x - x)
First, distribute the first term of the first binomial (x) to both terms of the second binomial:
x * 8x = 8x^2
x * (-x) = -x^2
Next, distribute the second term of the first binomial (6) to both terms of the second binomial:
6 * 8x = 48x
6 * (-x) = -6x
Now, let's combine the like terms:
8x^2 + (-x^2) + 48x + (-6x)
Simplify further:
8x^2 - x^2 + 48x - 6x
Combine the like terms:
7x^2 + 42x
So, multiplying the binomials (x + 6)(8x - x) gives the result 7x^2 + 42x.