Determine whether the following are perfect squares Determine whether the following are perfect squares. If so, fine the square root. 64 2. 36 3. 45 4. x2 5. y8 6. 4x6 7. 9y7 8. 49p10 Factor each trinomial. Check your answer. 9. 5x2 + 17x + 6 10. 2x2 + 5x – 12 11. 6x2 – 23x + 7 12. –4x2 + 11x + 20 13. –2x2 + 7x – 3 14. 8x2 + 27x + 9

Factoring Special Cases

Difference of Two Squares There are only two terms. The two terms are perfect squares. They are being subtracted.

Shortcut 9x2 – 4 Find the square root of each term and put them in parentheses like this: (3x 2)(3x 2) Put a + in one and a - in the other. (3x + 2)(3x - 2)

Perfect Square Trinomial It is a trinomial The first and last terms are perfect squares. Is the last term positive? Find the square root of the first and last terms, then multiply the results together and double it. Is this the middle term?

Shortcut 9x2 + 12x + 4 Find the square root of each term and put them in parentheses like this: (3x 2)(3x 2) Use the sign in front of the “b” term for both sets of parentheses. (3x + 2)(3x + 2) (3x + 2)2

Try these… 9x2 + 24x + 16 9x2 – 64 4x2 – 20x + 25 16x2 – 25 4a2 – 121b2 x2 – 6xy + 9y2 8x2 - 32 4x2 – 16x + 16

Remember: If you cannot remember the shortcuts… The old way still works. This is supposed to speed things up. Try it for a while, if you just cannot “get” one of them, use the old way.

A rectangular piece of cloth must be cut to make a tablecloth A rectangular piece of cloth must be cut to make a tablecloth. The area needed is (16x2 – 24x + 9) in2. The dimensions of the cloth are of the form cx – d, where c and d are whole numbers. Find an expression for the perimeter of the cloth. Find the perimeter when x = 11 inches. The tablecloth is a square with area (16x2 – 24x + 9) in2. P = 4s

Determine whether each trinomial is a perfect square. If so factor Determine whether each trinomial is a perfect square. If so factor. If not, explain. 64x2 – 40x + 25 2. 121x2 – 44x + 4 3. 49x2 + 140x + 100 4. A fence will be built around a garden with an area of (49x2 + 56x + 16) ft2. The dimensions of the garden are cx + d, where c and d are whole numbers. Find an expression for the perimeter when x = 5. Determine whether the binomial is a difference of two squares. If so, factor. If not, explain. 5. 9x2 – 144y4 6. 30x2 – 64y2 7. 121x2 – 4y8