Question

Part A: Determine if the expression is one of our special products. If so, identify it by its general form:

( a + b ) 2, ( a − b ) 2, or ( a + b ) ( a − b ). If not, write "not a special product."
Part B: If it's a special product, show the "shortcut" steps to multiply (remember how we did it in live session or review the problem shown above).
If it's not a special product, show the steps for multiplying polynomials.
Part C: Write your final answer in standard form - always in standard form, even if it's not stated.
1. ( x − 6 ) 2
2. ( x + 8 ) ( x + 1 )
3. ( 3 x + 2 ) ( 3 x + 2 )
4. ( 2 x − 7 ) ( 2 x + 7 )
5. (x-5) (2x-5)

Answer 1

1.

Part A: Yes, it is (a - b)².

Part B: a² - 2ab + b² => (x - 6)² = x² - 12x + 36.

Part C: x² - 12x + 36.

2.

Part A: Not a special product.

Part B: Binomial distribution => (x + 8)(x + 1) = x² + 9x + 8.

Part C: x² + 9x + 8.

3.

Part A: Yes, it is (a + b)²

Part B: a² + 2ab + b² => (3x + 2)² = 9x² + 12x + 4.

Part C: 9x² + 12x + 4.

4.

Part A: Yes, it is (a + b)(a - b), a difference of squares.

Part B: a² - b² => 4x² - 49

Part C: 4x² - 49

5.

Part A: Not a special product.

Part B: Binomial distribution => (x - 5)(2x - 5) = 2x² - 15x + 25.

Part C: 2x² - 15x + 25