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xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z
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20 May 2018, 14:13
20 May 2018, 14:13
Expert Reply
00:00
Question Stats:
90% (00:37) correct
9% (00:39) wrong based on 143 sessions
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Quantity A |
Quantity B |
\(xy^2z(x^2z + yz^2 - xy^2)\) |
\(x^3y^2z^2 + xy^3z^3 - x^2y^4z\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z
[#permalink]
28 Jun 2018, 16:31
28 Jun 2018, 16:31
2
sandy wrote:
Quantity A |
Quantity B |
\(xy^2z(x^2z + yz^2 - xy^2)\) |
\(x^3y^2z^2 + xy^3z^3 - x^2y^4z\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Here;
In statement 1 : \(xy^2z(x^2z + yz^2 - xy^2)\) = \(x^3y^2z^2 + xy^3z^3 - x^2y^4z\) = statement 2
Hence option C
Re: xy2z(x2z + yz2 - xy2) vs x3y2z2 + xy3z3 - x2y4z
[#permalink]
17 Jul 2018, 12:07
17 Jul 2018, 12:07
Expert Reply
Explanation
In Quantity A, the term xy2z on the outside of the parentheses must be multiplied by each of the three terms inside the parentheses. Then simplify the expression as much as possible.
Taking one term at a time, the first is \(xy^2z \times x^2z = x^3y^2z^2\), because there are three factors of x, two factors of y, and two factors of z. Similarly, the second term is \(xy^2z \times yz^2 = xy^3z^3\) and the third is \(xy^2z \times (-xy^2) = -x^2y^4z\).
Adding these three terms together gives the distributed form of Quantity A: \(x^3y^2z^2 + xy^3z^3 - x^2y^4z\).
This is identical to Quantity B, so the two quantities are equal.
In Quantity A, the term xy2z on the outside of the parentheses must be multiplied by each of the three terms inside the parentheses. Then simplify the expression as much as possible.
Taking one term at a time, the first is \(xy^2z \times x^2z = x^3y^2z^2\), because there are three factors of x, two factors of y, and two factors of z. Similarly, the second term is \(xy^2z \times yz^2 = xy^3z^3\) and the third is \(xy^2z \times (-xy^2) = -x^2y^4z\).
Adding these three terms together gives the distributed form of Quantity A: \(x^3y^2z^2 + xy^3z^3 - x^2y^4z\).
This is identical to Quantity B, so the two quantities are equal.
