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# GCSE Maths homework watch

1. Hi
Please can you explain how to work out the following question
Re-write x^2 + 8x + 1 in the form (x+a)^2+b
Thank you!
2. (Original post by Valiant_Pilot)
Hi
Please can you explain how to work out the following question
Re-write x^2 + 8x + 1 in the form (x+a)^2+b
Thank you!
Right. Given that (x+a)^2 ((x+a)(x+a)) is identical to x(x+a)+a(x+a), which expands to x^2+2ax+a^2, you can simply solve 2ax = 8x to get a. Expand (x+a)^2, with the value of a you just worked out, and see what you can do from there.
3. (Original post by _gcx)
Right. Given that (x+a)^2 ((x+a)(x+a)) is identical to x(x+a)+a(x+a), which expands to x^2+2ax+a^2, you can simply solve 2ax = 8x to get a. Expand (x+a)^2, with the value of a you just worked out, and see what you can do from there.
Thanks so much, this has really helped me!
4. (Original post by Valiant_Pilot)
Hi
Please can you explain how to work out the following question
Re-write x^2 + 8x + 1 in the form (x+a)^2+b
Thank you!
It's called 'difference of two squares':

You take half of the second term (leaving out the x) and stick it into the this bracket:

(X + 4)^2.

However when you expand this you get an extra 16, surplus to requirement. So you go (x + 4)^2 - 16 to compensate.

Now you add 1 like in the original equation

(x + 4)^2 - 16 + 1

= (x + 4)^2 - 15

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