Question

(а + 3)(а – 3) – (а – 2)^2

Answer 1

(а + 3)(а - 3) - (a - 2)² = a² - 3² - (a² - 4a + 4) = a² - 9 - a² + 4a - 4 = 4a - 13

Answer 2

(а+3)(а-3)-(а-2)²=
=а²+3а-3а-9-(а²+4-4а)=
=а²-9-а²-4+4а=
=4а-13

Answer 3

Let's simplify the expression step by step:

(а + 3)(а – 3) – (а – 2)^2

Step 1: Expand the first term (а + 3)(а – 3) using the distributive property (FOIL method): (а + 3)(а – 3) = а * а + а * (-3) + 3 * а + 3 * (-3) = а^2 - 3а + 3а - 9 = а^2 - 9

Step 2: Expand the second term (а – 2)^2 using the formula for squaring a binomial: (а – 2)^2 = (а – 2)(а – 2) = а * а + а * (-2) + (-2) * а + (-2) * (-2) = а^2 - 2а - 2а + 4 = а^2 - 4а + 4

Now, substitute these expansions back into the original expression:

(а + 3)(а – 3) – (а – 2)^2 = (а^2 - 9) - (а^2 - 4а + 4)

Next, remove the parentheses:

= а^2 - 9 - а^2 + 4а - 4

Now, combine like terms:

= (а^2 - а^2) + 4а - 9 - 4

The а^2 terms cancel out:

= 4а - 13

So, the simplified expression is 4а - 13.