How do you get this math question and whats the concept?

Question

x^2+8x+16
I'd like the answer and the concept. I know that the answer is (x+4)^2 , but how do you get rid of the 8x?

Answer 1

You need to factor out like terms... This is the "long way" to do it, but maybe it'll help you see better.

x^2 + 8x + 16
= x^2 + (4x + 4x) + 16
= (x^2 + 4x) + (4x + 16)
= x(x + 4) + 4(x + 4)
= (x + 4)(x + 4)
= (x + 4)^2

*****************
Maybe working backwards would help more.

(x + 4)^2
= (x + 4)(x + 4)
= (x)(x) + 4(x) + 4(x) + 4(4)
= x^2 + 4x + 4x + 16
= x^2 + 8x + 16

Answer 2

1) x^2 + 8x + 16

2) x^2 + 4x + 4x +16 --> because 4+4=8, and 4*4=16
3) (x^2 + 4x )+ (4x + 16) --> group together
4) x(x + 4) + 4(x + 4) --> this will be x^2 + 4x + 4x + 16 if you distribute, which is the second problem so that means it works.
5) (x + 4)(x + 4) --> you get this from part 4, and you just take the {x} and {+4} from outside the parenthesis and then the matching {x+4} inside the parenthesis to get this step of the problem.
6) (x + 4)^2 --> your answer.... :D

Answer 3

see step by step

u must be knowing the formula of (a+b)^2= a^2+b^2+2*a*b.

x^2+8x+16
now we can write the abv equation as
x^2+4^2 +2*x*4

so coparing it with the formula above we can get the result as (x+4)^2 ........... by puting a=x and b= 4.


(x+4)^2
now some more properties of this it has 2 equal roots because its D = 0

the graph is a upward opening parabola touching the axis at (2,0)

Answer 4

Its simply factorising the a quadratic expression. You need 2 numbers that multiply to equal 16 and add to equal 8, which is 4 and 4.
So it factorises to (x+4)(x+4), and then into (x+4)^2.

Hope that helped.

Answer 5

It's quite simple.....

You require numbers here that add up to 8, but also are factors of 16.
Factors of 16 are-:
1 and 16
8 and 2
4 and 4

Only the 4 and 4 option add up to 8, so we know this is the correct choice.

Answer 6

there is a formula to use for ax^2 + bx + c
(-b+- sqrt(b^2-4ac))/2. I cannot remember the exaxt formula but you should be able to find it. This gives the right answer.

Alternatively, you could simply find the factors of c that add to b and do it by trial and error.

Answer 7

You are multiplying incorrectly. The multiplication of (A+B)^2 follows this form:

(A+B)^2 = (A+B)*(A+B) = A^2 + A*B + B*A + B^2 = A^2 + 2*A*B + B^2

You can think of it using the distributive rule (I think that's the name):

(A+B)^2 = (A+B)*(A+B) = (A+B)*A + (A+B)*B = A^2 + A*B + B*A + B^2 = A^2 + 2*A*B + B^2

Answer 8

x^2+8x+16 = (x+a) * (x+b) = x^2 + (a+b) * x + ab

=>

a+b = 8

ab = 16

=>

a = b = 4

etc.

Answer 9

the formula is
(a+b)^2 = a^2+2*a*b+b^2
and if you have the equation then do the reverse