I need to multiply these two binomials together: (x-2)(x-1). Please explain how to do them as well. Thanks!

2 answers:

8 0

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)

Snezhnost [94]3 years ago

3 0

first multiply the second parenthesis by x then by -2:-

(x - 2)(x - 1)

= x(x - 1) - 2(x - 1)

= x^2 - x - 2x + 2

= x^2 - 3x + 2

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Learning Task 4. Solve the problem by applying the sum and product of roots

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Answer:

<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>

Step-by-step explanation:

For a quadratic equation:

$x^2+bx+c=0$

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

$x^2-18x+80=0$