c1 factorising question

Original post by ccfctom

Hello all I cant get my head around this question I think its just completing the square?

Factorise the following

(2x-1)^2 - x^2

I got (2x-1-x)(2x-1+x)

But have no idea if its right, could someone explain please? :smile:

That is correct - it's not completing the square, though! It's the difference of two squares.

Your expression can be made simpler - what is 2x-1+x?

Reply 2

OP

Original post by Smaug123

That is correct - it's not completing the square, though! It's the difference of two squares.

Your expression can be made simpler - what is 2x-1+x?

I see

So simplified its

(x-1) (3x-1) ?

Reply 3

Original post by ccfctom

I see

So simplified its

(x-1) (3x-1) ?

Indeed.

Reply 4

OP

Original post by Smaug123

Indeed.

Thanks

)

Reply 5

OP

Original post by ccfctom

Thanks

)

This one - (p+q)^2 - (p+r)^2

i got - (p+q+p+r) (p+q-p+r)

= (2p+q+r) (q+r)

I have a feeling this factorises further but not sure how to put it?

Reply 6

Original post by ccfctom

This one - (p+q)^2 - (p+r)^2

i got - (p+q+p+r) (p+q-p+r)

= (2p+q+r) (q+r)

I have a feeling this factorises further but not sure how to put it?

Your first step is wrong. (p+q)^2 - (p+r)^2 = ((p+q)+(p+r)) ((p+q)-(p+r)).

Reply 7

OP

Original post by Smaug123

Your first step is wrong. (p+q)^2 - (p+r)^2 = ((p+q)+(p+r)) ((p+q)-(p+r)).

Does it go further?

I ended up with (p(q+r)) (p(q-r))

Reply 8

Original post by ccfctom

Does it go further?

I ended up with (p(q+r)) (p(q-r))

The incorrect expression you came up with does not simplify further. However, it was incorrect. Note that -(p+r) is not the same as -p+r.

Reply 9

OP

Original post by Smaug123

The incorrect expression you came up with does not simplify further. However, it was incorrect. Note that -(p+r) is not the same as -p+r.

So the answer is

((p+q)+(p+r)) ((p+q)-(p+r)). ? Or does that simplify further (the one you said)

Reply 10

Original post by ccfctom

So the answer is

((p+q)+(p+r)) ((p+q)-(p+r)). ? Or does that simplify further (the one you said)

This is the answer, and it does simplify further.

Reply 11

OP

Original post by Smaug123

This is the answer, and it does simplify further.

How does it simplify? I cant figure it out

I got q(q+2p) - r(r+2p)

(edited 9 years ago)

Reply 12

davros

16

Original post by ccfctom

How does it simplify? I cant figure it out

I got q(q+2p) - r(r+2p)

How did you get that from the expression you posted earlier?

You should be looking to simplify the two outside brackets that you were multiplying together.

Reply 13

OP

this question (p+q)^2 - (p+r)^2

this is what I did

(p+q) (p+q) - (p+r) (p+r)

=(p^2 + pq + pq + q^2) - (p^2 + pr + pr + r^2)

= (2pq + q^2 ) - (2pr +r^2) (p^2 cancel each other so took out)

= q(q+2p) - r(r+2p)

Where have I gone wrong? could you post how to work it out properly?

(edited 9 years ago)

Reply 14

davros

16

Original post by ccfctom

this question (p+q)^2 - (p+r)^2

this is what I did

(p+q) (p+q) - (p+r) (p+r)

=(p^2 + pq + pq + q^2) - (p^2 + pr + pr + r^2)

= (2pq + q^2 ) - (2pr +r^2) (p^2 cancel each other so took out)

= q(q+2p) - r(r+2p)

Where have I gone wrong? could you post how to work it out properly?

What you've written isn't wrong, but it can be rearranged in a different way which makes the factorization clearer.

I would go back to your original expression and use the difference of two squares formula - then the factors will drop out automatically :smile:

Reply 15

OP

Original post by davros

What you've written isn't wrong, but it can be rearranged in a different way which makes the factorization clearer.

I would go back to your original expression and use the difference of two squares formula - then the factors will drop out automatically :smile:

its confusing me cause there's more terms like 58^2 - 57^2 is easy

(58+57) (58-57)
(115) (1)
=115

but this way I get

( (p+q)+ (p+r) ) ( (p+q) -(p+r) )

Not sure where to go from there

Reply 16