6.3 Trinomial Squares

1. 6.3 Trinomial Squares • Goals: To recognize a trinomial square and be able to factor it • Remember to always factor out a common factor before you see if it is a trinomial square or not!!

2. Multiply: (x + 3)2 x2 + 6x + 9 Multiply: (2x - 5)2 4x2 - 20x +25 Trinomial Squares

3. Trinomial Squaresx2 + 6x +94x2 – 20x + 25 • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

4. Is 4x2 – 20x + 25a Trinomial Square? Yes!! • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

5. Is x2 + 8x + 16a Trinomial Square? Yes!! • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

6. Is x2 - 12x + 4a Trinomial Square? no • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

7. Is 9x2 - 12x + 16a Trinomial Square? no • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

8. Is 9x2 + 24x - 16a Trinomial Square? no • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

9. Is 16x2 + 40xy + 25y2a Trinomial Square? yes • Two of the terms must be squares (A2 and B2) • No minus sign before A2 and B2 • If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

10. To Factor Trinomial Squares: • A2+ 2AB + B2(A + B)2 • A2- 2AB + B2(A - B)2 Factor: x2 + 10x + 25 (x + 5)2

11. To Factor Trinomial Squares: • A2+ 2AB + B2(A + B)2 • A2- 2AB + B2(A - B)2 Factor: x2 - 8x + 16 (x - 4)2

12. To Factor Trinomial Squares: • A2+ 2AB + B2(A + B)2 • A2- 2AB + B2(A - B)2 Factor: 4x2 + 12x + 9 (2x + 3)2

13. To Factor Trinomial Squares: • A2+ 2AB + B2(A + B)2 • A2- 2AB + B2(A - B)2 Factor: 2x2 + 12x + 18 2(x2 + 6x + 9) 2(x + 3)2

14. Factor: x2 - 8x + 16 Check your answer using FOIL (x – 4)(x – 4) x ( - )2 4

15. Factor: 4x2 + 12x + 9 (2x + 3)2

16. Factor: 9x2 + 30xy + 25y2 (3x + 5y)2

17. Factor: 2x2 + 12x + 18 2(x2 + 6x + 9) 2(x + 3)2

18. Assignment:Page 2714-42 even