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# x(x – y) – z(x – y) =

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
x(x – y) – z(x – y) =  [#permalink]

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01 Jun 2017, 12:10
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Difficulty:

5% (low)

Question Stats:

85% (00:54) correct 15% (01:29) wrong based on 87 sessions

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$$x(x – y) – z(x – y) =$$

(A) x – y
(B) x – z
(C) (x – y)(x – z)
(D) (x – y)(x + z)
(E) (x – y)(z – x)

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x(x – y) – z(x – y) =  [#permalink]

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01 Jun 2017, 13:13
Bunuel wrote:
$$x(x – y) – z(x – y) =$$

(A) x – y
(B) x – z
(C) (x – y)(x – z)
(D) (x – y)(x + z)
(E) (x – y)(z – x)

$$x(x – y) – z(x – y) =$$

Factor out $$(x - y)$$ to get

$$(x - y) (x - z)$$

To double check work

Prompt: $$x(x – y) – z(x – y) =$$

$$(x^2 - xy) - (xz - yz)$$=

$$x^2 - xy - xz + yz$$

Answer: $$(x - y) (x - z)$$ =

$$x^2 - xz - xy + yz$$ - rearrange the two inner terms and it's a match
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Re: x(x – y) – z(x – y) =  [#permalink]

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01 Jun 2017, 15:43
Bunuel wrote:
$$x(x – y) – z(x – y) =$$

(A) x – y
(B) x – z
(C) (x – y)(x – z)
(D) (x – y)(x + z)
(E) (x – y)(z – x)

Given $$x(x – y) – z(x – y) =$$
(x - y) is common factor, taking out the common factor we get;
(x - y)(x - z)
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Re: x(x – y) – z(x – y) =  [#permalink]

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05 Jun 2017, 16:20
Bunuel wrote:
$$x(x – y) – z(x – y) =$$

(A) x – y
(B) x – z
(C) (x – y)(x – z)
(D) (x – y)(x + z)
(E) (x – y)(z – x)

Let’s simplify the given expression:

x(x - y) - z(x - y)

Factoring out (x- y), we have:

(x - y)(x - z)

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Re: x(x – y) – z(x – y) =  [#permalink]

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05 Jun 2017, 16:29
Top Contributor
Bunuel wrote:
$$x(x – y) – z(x – y) =$$

(A) x – y
(B) x – z
(C) (x – y)(x – z)
(D) (x – y)(x + z)
(E) (x – y)(z – x)

The posters above me demonstrated the best/faster approach, BUT if you didn't think of that technique, you can still solve the question.
We're looking for an expression that is EQUIVALENT to x(x – y) – z(x – y)
So, for any set of values for x, y and z, the correct answer must evaluate to have the same value as x(x – y) – z(x – y)

So, let's plug in some values for x, y and z
Let's try x = 3, y = 1 and z = 10

First plug those values into the GIVEN expression.
We get: x(x – y) – z(x – y) = 3(3 – 1) – 10(3 – 1)
= 3(2) – 10(2)
= 6 - 20
= -14

So, the correct answer choice will be the one that evaluates to -14 when we plug in x = 3, y = 1 and z = 10
(A) x – y = 3 - 1 = 2. We want -14. ELIMINATE A
(B) x – z = 3 - 10 = -7. We want -14. ELIMINATE B
(C) (x – y)(x – z) = (3 - 1)(3 - 10) = (2)(-7) = -14. GREAT! KEEP C
(D) (x – y)(x + z) = (3 - 1)(3 + 10) = (2)(13)= 26. We want -14. ELIMINATE D
(E) (x – y)(z – x) = (3 - 1)(10 - 3) = (2)(7)= 14. We want -14. ELIMINATE E

By the process of elimination, the correct answer is

Cheers,
Brent

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Re: x(x – y) – z(x – y) =  [#permalink]

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06 Jun 2017, 06:38
2
Bunuel wrote:
$$x(x – y) – z(x – y) =$$

(A) x – y
(B) x – z
(C) (x – y)(x – z)
(D) (x – y)(x + z)
(E) (x – y)(z – x)

We need to rearrange the terms in order to get the desired option.
On opening the brackets and rearranging, we get

x^2 - xy - zx + zy = x^2 - zx -xy + zy = x(x - z) - y(x - z) = (x - z)(x - y)

Correct Option C
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Re: x(x – y) – z(x – y) =  [#permalink]

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09 Feb 2019, 13:09
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Re: x(x – y) – z(x – y) =   [#permalink] 09 Feb 2019, 13:09
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