false or true?

As always, Algebra wizard!!.

(a + 5)²   =  (a + 5)(a + 5)  =  a(a) + (a)(5) + (5)(a) + (5)(5)  =  a² + 5a + 5a + 25  =  a² + 10a + 25

(a - 5)²   =  (a - 5)(a - 5)  =  a(a) + (a)(-5) + (-5)(a) + (-5)(-5)  =  a² - 5a - 5a + 25  =  a² - 10a + 25

(a +5)² - (a - 5)²  = [a² + 10a + 25] - [a² - 10a + 25]  =  a² + 10a + 25 - a² + 10a - 25  =  20a

Yes; it's correct!

Simplify the following:

(a+5)^2-(a-5)^2

(a+5) (a+5) = (a) (a) + (a) (5) + (5) (a) + (5) (5) = a^2+5 a+5 a+25 = a^2+10 a+25:

a^2+10 a+25-(a-5)^2

(a-5) (a-5) = (a) (a) + (a) (-5) + (-5) (a) + (-5) (-5) = a^2-5 a-5 a+25 = a^2-10 a+25:

25+10 a+a^2-a^2-10 a+25

-(a^2-10 a+25) = -a^2+10 a-25:

25+10 a+a^2+-a^2+10 a-25

Grouping like terms, 25+10 a+a^2-25+10 a-a^2 = (10 a+10 a)+(a^2-a^2)+(25-25):

(10 a+10 a)+(a^2-a^2)+(25-25)

10 a+10 a = 20 a:

20 a+(a^2-a^2)+(25-25)

a^2-a^2 = 0:

20 a+(25-25)

25-25 = 0:

Answer: |20a     IT IS TRUE!!.

Note :

(a + 5)^2  - (a - 5)^2   factors as a difference of squares   =

[ (a + 5)  - (a - 5)]  [(a + 5) + (a - 5) ]  =

[ 10] [ 2a]  =

20a