Someone help cant think (1 Viewer)

[JusD]

Ok I need to 'add a term to form a perfect square'. The book I have has no working out so could you explain how you are getting your answer.

4a^2 - 4a

Thanks

 

[DownInFlames]

add 1

from 4a^2 - 4a:
1. (2a - )(2a - )

2. (2a - 1)(2a - 1)

3. 4a^2 - 4a + 1

 

[a-n-d-r-e-w]

if u dont understand how down in flames worked out the answer, you need to half the coefficient of the 2nd term then square it, this number should equal the product of the first and 3rd term. i.e. to say

4a^2-4a ----> -4/2= -2---> -2^2=4
4 x some number = 4
therefore the number you need to add is 1
I hope that makes it easier to understand

 

[vds700]

to complete the square of any quadratic, i always take the coeffivient of a^2 out.

ie 4a^2 -4a = 4(a^2 - a)

now to complete the square of the inside bit, u just halve the coeeficient of the a term and square it.

(-1/2)^2 = 1/4, add this to the inside of the brackets

the equation becomes
4(a^2 - a + 1/4)
=4a^2 - 4a + 1

 

[lyounamu]

4a^2 - 4a = 4(a^2 - a)
= 4(a^2 - a + 1/4) - 1
= 4 (a - 1/2)^2 - 1

 

[lyounamu]

add 1

from 4a^2 - 4a:
1. (2a - )(2a - )

2. (2a - 1)(2a - 1)

3. 4a^2 - 4a + 1

When you add 1, you need to offset that 1 by putting -1.