Algebraic Expression Misconception

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lewis.h
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#1
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#1
x is not 0.


16x^2 is the numerator of the first fraction and 2x + 1.25 is the denominator of the first fraction, 25 is the numerator of the 2nd fraction and 8x + 5 is the denominator of the 2nd fraction.


Prove that the algebraic expression can be written in the form ax-b where a and b are integers.

I did it and got 2x-5 by cross simplifying the 16x^2 to get 4x^2 , and then subtracting the 5.

The mark scheme got 8x - 5 by multiplying 16x^2 by 4, and square rooting it to get 8x, and then subtracting the 5 to get 8x - 5.

I understand the logic in their method, but why is mine wrong ?
Last edited by lewis.h; 3 years ago
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T!gger34
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#2
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#2
Are you adding, subtracting, multiplying or dividing these fractions?
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lewis.h
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#3
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#3
(Original post by dextrous63)
Are you adding, subtracting, multiplying or dividing these fractions?
Subtracting them.
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T!gger34
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#4
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#4
Just to be sure of the original expression, is it this?
(16x^2)/(2x+1.25)-25/(8x+5)

Since that's what you've described.
Last edited by dextrous63; 3 years ago
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lewis.h
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#5
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#5
(Original post by dextrous63)
Just to be sure of the original expression, is it this?
(16x^2)/(2x+125)-25/(8x+5)

Since that's what you've described.
It’s 1.25 not 125
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username1732133
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#6
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#6
(Original post by lewis.h)
x is not 0.


16x^2 is the numerator of the first fraction and 2x + 1.25 is the denominator of the first fraction, 25 is the numerator of the 2nd fraction and 8x + 5 is the denominator of the 2nd fraction.


Prove that the algebraic expression can be written in the form ax-b where a and b are integers.

I did it and got 2x-5 by cross simplifying the 16x^2 to get 4x^2 , and then subtracting the 5.

The mark scheme got 8x - 5 by multiplying 16x^2 by 4, and square rooting it to get 8x, and then subtracting the 5 to get 8x - 5.

I understand the logic in their method, but why is mine wrong ?
\frac{16x^2}{2x+1.25}-\frac{25}{8x+5}

Multiply the numerator and denominator of the first fraction by 4.

=\frac{64x^2}{8x+5}-\frac{25}{8x+5}

=\frac{16x^2-25}{8x+5}

Recognise that the numerator is a difference of two squares.

=\frac{(8x+5)(8x-5)}{8x+5}

Divide the numerator and denominator by 8x+5

=8x-5
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T!gger34
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#7
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#7
(Original post by lewis.h)
It’s 1.25 not 125
Thanks. Have amended it. Although Bury Tutor has solved it, as indeed the markscheme did (assuming these are pretty much the same, nobody "square rooted" anything in the way you describe, but they did factorise the difference of 2 squares), it would be useful if you could post what you actually wrote so that we can look for any errors.
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lewis.h
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#8
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#8
(Original post by dextrous63)
Thanks. Have amended it. Although Bury Tutor has solved it, as indeed the markscheme did (assuming these are pretty much the same, nobody "square rooted" anything in the way you describe, but they did factorise the difference of 2 squares), it would be useful if you could post what you actually wrote so that we can look for any errors.
I have just looked over it and now I’ve realised my error.

I didn’t multiply 16x^2 by 4.

Thanks though.
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T!gger34
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#9
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#9
(Original post by lewis.h)
I have just looked over it and now I’ve realised my error.

I didn’t multiply 16x^2 by 4.

Thanks though.
Excellent. The devil is in the detail
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