y = (x2 – 2x + 1) y = (x – 1)(x – 1) Prove that the following functions are equivalent through algebraic and numerical proof

Question

y = (x2 – 2x + 1)
y = (x – 1)(x – 1)
Prove that the following functions are equivalent through algebraic and numerical proof

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5 months 2021-09-05T00:53:41+00:00 2 Answers 3 views 0

1. y = (x^2 – 2x + 1)

y = (x – 1)(x – 1)

Algebraic Proof

FOIL y = (x – 1)(x – 1)

y = (x – 1) (x -1 ) = x^2 -2x + 1

Done.

Numeric Proof

Let x = 1

y = x^2 – 2x + 1

y = (1)^2 – 2(1) + 1

y = 1 – 2 + 1

y = 2 + 2

y = 0

Let x be 1 again.

y = (x – 1)(x – 1)

y = (1 – 1)(1 – 1)

y = 0

There you have it. Both equations are the same.

see below

Step-by-step explanation:

y = (x² – 2x + 1)

y = (x – 1)(x – 1)

First, recognize that the first equation is fully simplified/expanded already.

Now, we should solve for the second equation.

FOIL the expressions: first–outer–inner–last

(x – 1)(x – 1)

F: x²

O: -x

I: -x

L: 1

Combine these terms.

x² – x – x + 1

x² – 2x + 1

Notice that this equation is identical to our first equation. Therefore, the functions are equivalent.

Hope this helps!