Completing the square

[bobisaka]

Hi guys,

I am unsure as to how to solve the radical in the numerator.
I have used symbolab calculator, after multiplying the parenthesis by the exponent, for the numerator I do not understand how the square of 13 became the 2 times the square root of 13?

I would calculate the numerator in the parenthesis as (1+13).

 

[lev888]

Hi guys,

I am unsure as to how to solve the radical in the numerator.
I have used symbolab calculator, after multiplying the parenthesis by the exponent, for the numerator I do not understand how the square of 13 became the 2 times the square root of 13?

I would calculate the numerator in the parenthesis as (1+13).

The line highlighted in red? This is just (a-b)^2 = a^2 - 2ab + b^2.

 

[Dr.Peterson]

Hi guys,

I am unsure as to how to solve the radical in the numerator.
I have used symbolab calculator, after multiplying the parenthesis by the exponent, for the numerator I do not understand how the square of 13 became the 2 times the square root of 13?

I would calculate the numerator in the parenthesis as (1+13).

This is wrong:

When you square a binomial, you don't just square each term; [imath](a+b)^2\ne a^2+b^2[/imath], but rather [imath](a+b)(a+b) = a^2+2ab+b^2[/imath].

 

[tkhunny]

How would you multiply 23*23 = 23^2? 2^2 + 3^3 = 4 + 9 = 13. Hmm... That doesn't seem to work

How about 20*(23) + 3*23 - 460 + 69 = 529... That seems better.

Maybe (20 + 3)*(20 + 3) = 400 + 60 + 60 + 9 = 529... Now we're getting somewhere.

It is NO difference with variable names. Use the Distributive Property.

 

[Steven G]

2*(2/3) is NOT 1/3. When you multiply a positive number by 2, the number get larger!. So 2*2/3 must be larger than 2/3. 1/3 < 2/3!
2*2/3 = 4/3.

(1/2)*(2/3) = 1/3. Sure, (1/2)(2/3) = 2/6 = 1/3 but reducing 1st is easier.