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1. Simplify the expression:
[tex]\[ B = (x-3)^2 - (x-1)^2 + 4x \][/tex]

a) 1

b) 2

c) 3

d) 7

e) 8

Sagot :

GinnyAnswer
Sure, let's work through the given expression step by step to simplify it.

We start with the given expression:

[tex]\[ B = (x-3)^2 - (x-1)^2 + 4x \][/tex]

First, let's expand both squared terms:

1. Expanding [tex]\((x-3)^2\)[/tex]:

[tex]\[ (x-3)^2 = x^2 - 6x + 9 \][/tex]

2. Expanding [tex]\((x-1)^2\)[/tex]:

[tex]\[ (x-1)^2 = x^2 - 2x + 1 \][/tex]

Now substituting these expanded forms back into the original expression, we have:

[tex]\[ B = (x^2 - 6x + 9) - (x^2 - 2x + 1) + 4x \][/tex]

Next, distribute the negative sign across the second quadratic expression:

[tex]\[ B = x^2 - 6x + 9 - x^2 + 2x - 1 + 4x \][/tex]

Combine the like terms by adding or subtracting the coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant terms:

- The [tex]\(x^2\)[/tex] terms: [tex]\(x^2 - x^2 = 0\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(-6x + 2x + 4x = 0\)[/tex]
- The constant terms: [tex]\(9 - 1 = 8\)[/tex]

Therefore, the expression simplifies to:

[tex]\[ B = 0 + 0 + 8 \][/tex]

Thus,

[tex]\[ B = 8 \][/tex]

So, the correct answer is:

e) 8
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