Question

How can (a+3)2=a2+6a+9 be derived from the polynomial identity (a−3)2=a2−6a+9?

Answer 1

By writing the positive 3 as -(-3), and using the square of the difference, we get:

(a + 3)^2 =  a^2 + 6a + 9

How can we derive the expansion?

The expansion for the square of the difference between two values is:

(a - b)^2  = a^2 + b^2 - 2ab

Which is the one used for:

(a−3)^2 = a^2−6a + 9

Now, if instead of "-3" we write -(-3) (which is equal to positive 3, as in the first expression) we can rewrite:

(a + 3)^2 = (a - (-3))^2 = a^2 - 2*(-3)*a + (-3)^2

                                  = a^2 + 6a + 9

Which is what we wanted to get.

If you want to learn more about polynomial expansions:

https://brainly.com/question/13602562

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