We need to factor the quadratic expressions given in problems 22, 23, 25, 26, 28, and 29.

1. Problem Description

We need to factor the quadratic expressions given in problems 22, 23, 25, 26, 28, and

2

9.

2. Solution Steps

Problem 22: $y^2 + 2y + 1$

This is a perfect square trinomial.

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

In this case, $a=y$ and $b=1$.

Therefore, $y^2 + 2y + 1 = (y+1)^2 = (y+1)(y+1)$.

Problem 23: $y^2 - 3y - 28$

We need to find two numbers that multiply to -28 and add to -

3. These numbers are -7 and

4. Therefore, $y^2 - 3y - 28 = (y-7)(y+4)$.

Problem 25: $x^2 - 8x - 240$

We need to find two numbers that multiply to -240 and add to -

8. These numbers are -20 and

1

2. Therefore, $x^2 - 8x - 240 = (x-20)(x+12)$.

Problem 26: $x^2 - 26x + 165$

We need to find two numbers that multiply to 165 and add to -

2

6. These numbers are -11 and -

1

5. Therefore, $x^2 - 26x + 165 = (x-11)(x-15)$.

Problem 28: $x^2 - 49$

This is a difference of squares.

$a^2 - b^2 = (a-b)(a+b)$

In this case, $a=x$ and $b=7$.

Therefore, $x^2 - 49 = (x-7)(x+7)$.

Problem 29: $x^2 - 9$

This is a difference of squares.

$a^2 - b^2 = (a-b)(a+b)$

In this case, $a=x$ and $b=3$.

Therefore, $x^2 - 9 = (x-3)(x+3)$.

3. Final Answer

2

2. $(y+1)(y+1)$

2

3. $(y-7)(y+4)$

2

5. $(x-20)(x+12)$

2

6. $(x-11)(x-15)$

2

8. $(x-7)(x+7)$

2

9. $(x-3)(x+3)$