Verified answer

Answer:

Sure! Let's factorize the given expressions using identities:

1) 81a² - 25b²

This expression can be factorized using the difference of squares identity:

(9a + 5b)(9a - 5b)

2) 0.49x²y² - 0.81

This expression can be factorized using the difference of squares identity:

(0.7xy - 0.9)(0.7xy + 0.9)

3) 16m²/49 - 25n²/121

This expression can be factorized using the difference of squares identity:

(4m/7 - 5n/11)(4m/7 + 5n/11)

4) 121 - 110m + 25m²

This expression is a perfect square trinomial and can be factorized as:

(11 - 5m)(11 - 5m)

5) 0.09a² + 0.3ab + 0.25b²

This expression can be factorized as a perfect square trinomial:

(0.3a + 0.5b)(0.3a + 0.5b)

6) (a + 3c)² - 1

This expression can be factorized using the difference of squares identity:

[(a + 3c) - 1][(a + 3c) + 1]

(a + 3c - 1)(a + 3c + 1)

7) x² - 2 + 1/x²

This expression can be factorized using the difference of squares identity:

(x - 1/x)(x + 1/x)

8) 1 - a² - 2ab - b²

This expression can be factorized as a difference of squares:

(1 - a - b)(1 + a + b)

9) 16 - 9(a + b)²

This expression can be factorized using the difference of squares identity:

(4 - 3(a + b))(4 + 3(a + b))

10) 16a⁴ - 81

This expression can be factorized using the difference of squares identity:

(4a² - 9)(4a² + 9)

Please Mark Me As Brainlist...!!

Answer:

Sure, here are the factorizations of the given expressions using identities:

**1) 81a² - 25b²**

This is a difference of squares, so we can factor it as:

```

(9a - 5b)(9a + 5b)

```

**2) 0.49x²y² - 0.81**

We can rewrite this expression as:

```

(0.7xy)² - (0.9)²

```

This is again a difference of squares, so we can factor it as:

```

(0.7xy - 0.9)(0.7xy + 0.9)

```

**3) 16m²/49 - 25n²/121**

We can rewrite this expression as:

```

(4m/7)² - (5n/11)²

```

This is also a difference of squares, so we can factor it as:

```

(4m/7 - 5n/11)(4m/7 + 5n/11)

```

**4) 121 - 110 m + 25m²**

We can rewrite this expression as:

```

11² - 110m + 25m²

```

This is of the form a² - 2ab + b², which can be factored as:

```

(a - b)²

```

Substituting back, we get:

```

(11 - 5m)²

```

**5) 0.09 a² + 0.3 a b + 0.25 b²**

We can rewrite this expression as:

```

(0.3a)² + 2(0.3a)(0.5b) + (0.5b)²

```

This is of the form a² + 2ab + b², which can be factored as:

```

(a + b)²

```

Substituting back, we get:

```

(0.3a + 0.5b)²

```

**6) (a+3c)² - 1**

This is of the form a² - 2ab + b² - 1, which can be factored as:

```

(a - b - 1)(a - b + 1)

```

Substituting back, we get:

```

(a + 3c - 1)(a + 3c + 1)

```

**7) x² - 2 + 1/x²**

We can rewrite this expression as:

```

x² - 2 + x^{-2}

```

This is of the form a² - 2ab + b², which can be factored as:

```

(a - b)(a - b)

```

Substituting back, we get:

```

(x - 1/x)(x - 1/x)

```

**8) 1 - a² - 2ab - b²**

This is of the form a² - 2ab + b² - 1, which can be factored as:

```

(a - b - 1)(a - b + 1)

```

Substituting back, we get:

```

(1 - a - b)(1 - a + b)

```

**9) 16 - 9 (a + b)²**

We can rewrite this expression as:

```

4² - 3² (a + b)²

```

This is of the form a² - b², which can be factored as:

```

(a - b)(a + b)

```

Substituting back, we get:

```

(4 - 3(a + b))(4 + 3(a + b))

```

**10) 16a4 - 81**

This is of the form a⁴ - b⁴, which can be factored as:

```

(a² - b²)(a² + b²)

```

Substituting back, we get:

```

(4a² - 9)(4a² + 9)

```