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The image you provided includes a worksheet on factoring algebraic expressions using algebraic identities. I'll go through each problem, solve it, and explain the steps.

### 1. \( 81 - x^2 \)
This expression is a difference of squares:
\[
81 - x^2 = (9 - x)(9 + x)
\]

### 2. \( y^2 - 64 \)
Again, a difference of squares:
\[
y^2 - 64 = (y - 8)(y + 8)
\]

### 3. \( d^2 - 9 \)
Difference of squares:
\[
d^2 - 9 = (d - 3)(d + 3)
\]

### 4. \( \frac{1}{x^2} - y^2 \)
This is also a difference of squares:
\[
\frac{1}{x^2} - y^2 = \left( \frac{1}{x} - y \right)\left( \frac{1}{x} + y \right)
\]

### 5. \( m^2 - 36 \)
Difference of squares:
\[
m^2 - 36 = (m - 6)(m + 6)
\]

### 6. \( y^9 - 144 \)
This is not a standard difference of squares or cubes. However, the expression can be simplified using factoring methods beyond algebraic identities, such as trial and error or more advanced techniques like finding factors of constants. Here, it's left as \( y^9 - 144 \).

### 7. \( 4 - q^2 \)
Difference of squares:
\[
4 - q^2 = (2 - q)(2 + q)
\]

### 8. \( x^2 - y^2 \)
Another classic difference of squares:
\[
x^2 - y^2 = (x - y)(x + y)
\]

### 9. \( z^2 - 1 \)
Difference of squares:
\[
z^2 - 1 = (z - 1)(z + 1)
\]

### 10. \( 25 - p^2 \)
Difference of squares:
\[
25 - p^2 = (5 - p)(5 + p)
\]

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Here are five related questions to practice:
1. Factor \( 49 - x^2 \).
2. Factor \( a^2 - 16b^2 \).
3. Simplify \( 100 - c^2 \).
4. Solve \( z^4 - 81 \).
5. Factor \( x^2 - 49y^2 \).

**Tip**: Whenever you see two squares subtracted, check if it's a difference of squares, which factors as \( (a - b)(a + b) \).

Factor each expression using algebraic identity.

This page covers how to factor algebraic expressions using algebraic identities such as the difference of squares. Learn to solve problems like 81 - x^2, y^2 - 64, and more. Suitable for Grades 9-10.

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