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3 years ago

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Write an equivalent expression for (x-3)(x-2)

2 answers:

Setler79 [48]3 years ago

8 0

(x - 3)(x - 2)

Solve using the FOIL method.

First
Outside
Inside
Last

We will be multiplying. Using FOIL, we will be multiplying the first numbers, outside numbers, inside numbers, and last numbers. This is how your steps should look like:

x * x
x * -2
-3 * x
-3 * -2

After using the FOIL method, rewrite the expression.

x² - 2x - 3x + 6

There is one more step to making sure the expression is fully simplified. We will be combining like terms. The like terms are -2x and -3x, so combine and simplify the expression.

<h3>x² - 5x + 6</h3>

is your answer by using the FOIL method to solve.

Anastaziya [24]3 years ago

6 0

This expression is factored completely. However, if we foil, we can make it to it's original expression.

When you foil, you get:

$x^2-2x-3x+6$

Simplify.

$x^2-5x+6$

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Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x

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Answer: The correct line is

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:

$\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.$

We are to select one of the lines from above that represent three equivalent expressions.

We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.

We have

$\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),$

and

$x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.$

So,

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Thus, Line 1 contains three equivalent expressions.

Now,

$\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),$

and

$x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.$

So,

$\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.$

Thus, Line 2 does not contain three equivalent expressions.

Hence, Line 1 is correct.

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