Question

2) a2 + 8ab + 16b2 - 1;​

Answer 1

Ответ:

$(a+4b)^{2}$ - 1

Объяснение:

Воспользуемся ФСУ (формула сокращенного умножения):

$(a+b)^{2}$ = $a^{2}$ + 2ab + $b^{2}$

$a^{2}$ + 8ab + 16$b^{2}$ - 1 =$(a+4b)^{2}$- 1

Answer 2

The expression you provided is a quadratic expression, which can be factored as follows:

a^2 + 8ab + 16b^2 - 1

This expression can be factored using the perfect square trinomial pattern. Notice that the first three terms (a^2 + 8ab + 16b^2) form a perfect square trinomial, specifically (a + 4b)^2. So, we can rewrite the expression as:

(a + 4b)^2 - 1

Now, we have the difference of two squares, which can be factored as follows:

[(a + 4b) + 1][(a + 4b) - 1]

So, the factored form of the expression is:

[(a + 4b) + 1][(a + 4b) - 1]

You can further simplify this if needed, but this is the factored form of the given expression.