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!!

Multiply: (x + 3) 2 x2x x Multiply: (2x - 5) 2 4x x Trinomial Squares

Trinomial Squares x 2 + 6x +9 4x 2 – 20x + 25 a.Two of the terms must be squares (A 2 and B 2 ) b.No minus sign before A 2 and B 2 c.If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative)

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

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

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

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

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

Is 16x xy + 25y 2 a Trinomial Square? a.Two of the terms must be squares (A 2 and B 2 ) b.No minus sign before A 2 and B 2 c.If we multiply “A” and “B”, then double the result, we get the middle term, “2AB” (or its negative) yes

To Factor Trinomial Squares: A 2 + 2AB + B 2  (A + B) 2 A 2 - 2AB + B 2  (A - B) 2 Factor: x x + 25 (x + 5) 2

To Factor Trinomial Squares: A 2 + 2AB + B 2  (A + B) 2 A 2 - 2AB + B 2  (A - B) 2 Factor: x 2 - 8x + 16 (x - 4) 2

To Factor Trinomial Squares: A 2 + 2AB + B 2  (A + B) 2 A 2 - 2AB + B 2  (A - B) 2 Factor: 4 x x + 9 (2x + 3) 2

To Factor Trinomial Squares: A 2 + 2AB + B 2  (A + B) 2 A 2 - 2AB + B 2  (A - B) 2 Factor: 2x x (x + 3) 2 2(x 2 + 6x + 9)

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

Factor: 4 x x + 9 (2x + 3) 2

Factor: 9x xy + 25y 2 (3x + 5y) 2

Factor: 2x x (x + 3) 2 2(x 2 + 6x + 9)

Assignment: Page even