show that a-b squared =a squared- 2ab + b squared is an identity when:
a= -3
b= 7
and when
a=-5
b=-10
(-3 - 7)^2 = -3^2 - 2(-3)(7) + 7^2
-10^2 = 9 + 42 + 49
100 = 100
(-5 - -10)^2 = -5^2 - 2(-5)(-10) + -10^2
5^2 = 25 - 100 + 100
25 = 25
Just a basic substitution problem. As long as you don't mix up the order of operations and positive/negative signs it's very straightforward.
This can be proven algebraically as true for all values of a and b. Just foil out (a - b)^2
a * a + a * -b + -b * a + -b * -b
a^2 + -ab + -ab + b^2
a^2 -2ab + b^2
(-3-7)^2=-3^2-(2x-3x7)+7
-10^2=9+42+7
100=100
I don't know why they bothered with those pairs of numbers - it is an identity PERIOD.
Comments
(-3 - 7)^2 = -3^2 - 2(-3)(7) + 7^2
-10^2 = 9 + 42 + 49
100 = 100
(-5 - -10)^2 = -5^2 - 2(-5)(-10) + -10^2
5^2 = 25 - 100 + 100
25 = 25
Just a basic substitution problem. As long as you don't mix up the order of operations and positive/negative signs it's very straightforward.
This can be proven algebraically as true for all values of a and b. Just foil out (a - b)^2
a * a + a * -b + -b * a + -b * -b
a^2 + -ab + -ab + b^2
a^2 -2ab + b^2
(-3-7)^2=-3^2-(2x-3x7)+7
-10^2=9+42+7
100=100
I don't know why they bothered with those pairs of numbers - it is an identity PERIOD.