Question

date: ____________ bell: ____ homework 6: factoring difference of squares
directions: factor each polynomial, if possible. check your answer using foil.

1. ( x^2 - 36 )
2. ( a^2b^2 - 100 )
3. ( 16y^2 - 25 )
4. ( y^2 + 49 )
5. ( 9a^2 - 121 )
6. ( 196 - x^2 )
7. ( 4y^2 - 81 )
8. ( 36c^2 - d^2 )
9. ( 16m^2 - p^2 )
10. ( m^4 - 64n^2 )
11. ( 1 - 4a^2 )
12. ( 9v^4 - 100 )

directions: factor each polynomial. look for a gcf first.

1. ( 3p^2 - 75 )
2. ( 5x^2 - 80 )
3. ( 7n^2 - 7 )
4. ( 16x^3 - 100x )
5. ( 3x^2 - 3y^2 )
6. ( 8a^2 - 18b^2 )
7. ( 4r^4 - 144 )
8. ( 81m^4 - m^2 )
9. ( 3k^4 - 48k^2 )
10. ( 2x^3 - 200x )
11. ( a^3 - a )
12. ( 32x^2 - 18y^2 )

Explanation:

Let's solve problem 1: \( x^2 - 36 \) using the difference of squares formula.

Step 1: Recall the difference of squares formula

The difference of squares formula is \( a^2 - b^2 = (a + b)(a - b) \).

Step 2: Identify \( a \) and \( b \)

For the polynomial \( x^2 - 36 \), we can rewrite it as \( x^2 - 6^2 \). So, \( a = x \) and \( b = 6 \).

Step 3: Apply the formula

Using the difference of squares formula, we substitute \( a = x \) and \( b = 6 \) into \( (a + b)(a - b) \). This gives us \( (x + 6)(x - 6) \).

Answer:

\( (x + 6)(x - 6) \)