Question

1) 81n²-36= 2) 169a⁴-64b²= 3) -0,09a^10b^6+1=

Answer 1

Ответ:

1) 9(3n-2)×(3n+2)

2)(13a²-8b)×(13a²+8b)

Пошаговое объяснение:

3‍♀️

Answer 2

Let's simplify these equations:

1. $81n^2 - 36$

First, notice that both terms are perfect squares:

$81n^2$ is $(9n)^2$, and $36$ is $6^2$.

So, we can rewrite the equation as:

$(9n)^2 - 6^2$

Now, we can apply the difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$

In this case, $a = 9n$ and $b = 6$:

$(9n + 6)(9n - 6)$

So, $81n^2 - 36$ factors as $(9n + 6)(9n - 6)$.

2. $169a^4 - 64b^2$

Again, notice that both terms are perfect squares:

$169a^4$ is $(13a^2)^2$, and $64b^2$ is $(8b)^2$.

So, we can rewrite the equation as:

$(13a^2)^2 - (8b)^2$

Now, we can apply the difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$

In this case, $a = 13a^2$ and $b = 8b$:

$(13a^2 + 8b)(13a^2 - 8b)$

So, $169a^4 - 64b^2$ factors as $(13a^2 + 8b)(13a^2 - 8b)$.

3. $-0.09a^{10}b^6 + 1$

This equation does not appear to factor easily using simple algebraic techniques. However, we can simplify it by factoring out a common factor of $0.09$ from both terms:

$-0.09a^{10}b^6 + 1 = 0.09(-a^{10}b^6 + \frac{1}{0.09})$

Now, we can focus on the expression inside the parentheses:

$-a^{10}b^6 + \frac{1}{0.09}$

You can leave it in this form, or if you want to simplify further, you can calculate $\frac{1}{0.09}$ to get a numerical value and then rewrite the expression accordingly.