The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

Algebraic Expression Misconception

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 ?
(edited 4 years ago)
Are you adding, subtracting, multiplying or dividing these fractions?
Reply 2
Avatar for lewis.h
lewis.h
OP
12
Original post by dextrous63
Are you adding, subtracting, multiplying or dividing these fractions?


Subtracting them.
Just to be sure of the original expression, is it this?
(16x2)/(2x+1.25)−25/(8x+5)(16x^2)/(2x+1.25)-25/(8x+5)

Since that's what you've described.
(edited 4 years ago)
Reply 4
Avatar for lewis.h
lewis.h
OP
12
Original post by dextrous63
Just to be sure of the original expression, is it this?
(16x2)/(2x+125)−25/(8x+5)(16x^2)/(2x+125)-25/(8x+5)

Since that's what you've described.


It’s 1.25 not 125
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 ?


16x22x+1.25−258x+5\frac{16x^2}{2x+1.25}-\frac{25}{8x+5}

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

=64x28x+5−258x+5=\frac{64x^2}{8x+5}-\frac{25}{8x+5}

=16x2−258x+5=\frac{16x^2-25}{8x+5}

Recognise that the numerator is a difference of two squares.

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

Divide the numerator and denominator by 8x+58x+5

=8x−5=8x-5
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.
Reply 7
Avatar for lewis.h
lewis.h
OP
12
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. :tongue:

Thanks though.
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. :tongue:

Thanks though.

Excellent. The devil is in the detail :wink:

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you