Ineed to multiply these two binomials together: (x-2)(x-1). explain how to do them as well.

There are 2 methods of completing this problem: FOIL and double distribution. They both will come up with the same answer, and will show you both methods.

FOIL:

FOIL stands for First, Outer, Inner, and Last and they are the positions within the binomials. Here is how to do that:

Firsts - the 1st term of each binomial - x * x = x^2

Outer - the ones on the outside of the binomial group - x * -1 = -x

Inner - ther terms that are closest to the inside parenthesis - -2 * x = -2x

Lasts - The last term in each binomial - -2 * -1 = 2

Now add them together: x^2 -x - 2x + 2 = x^2 -3x + 2 (Final answer)

Double distribution:

(x - 2)(x - 1)

x(x - 1) - 2(x - 1) (Distribute the (x -1) across the 1st binomial

x^2 - x - 2x + 2 (Distribute again for each set of terms)

x^2 - 3x + 2 (Simplify)

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

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