Squared binomial paradox?

Question

When you square this $$(5-2)^2$$ you will get 49 $$ 5^2 - 2 * 5 * (-2) + (-2)^2$$ $$25 + 20 + 4 = 49$$ but if you do it like this (5-2) * (5-2) you will get 9 $$ 5(5-2) - 2(5-2)$$ $$25-10-10+4$$ $$25-20+4$$ $$5+4$$ $$9$$ Why do I always get different results if I'm doing the same thing?Am I doing something wrong?

Answer 1

The binomial formular is $(a + b)^2 = a^2 + 2ab + b^2$

If you apply it:

$$(5 - 2)^2 = 5^2 + 2\cdot5\cdot(-2) + 2^2 = 25-20 + 4 = 9$$

The second binomial formular is $(a - b)^2 = a^2 - 2ab + b^2$

If you apply it:

$$(5 - 2)^2 = 5^2 - 2\cdot5\cdot 2 + 2^2 = 25-20 + 4 = 9$$

Your mistake was, that you used the second binomial formular but took $a$ as $-2$ instead as $2$.

Answer 2

You have actually done a blunder !!

$(5-2)^2=5^2-(2\times5\times2)+(-2)^2=25-20+4=9.$

Note that $(a-b)^2=a^2-2ab+b^2$