J17

1. (x + 3)(x + 1) 2. (x + 2)(x – 4)
3. (x – 7)(x + 3) 4. (x – 4)(x – 3)
5. (a + 8)(a – 3) 6. (p + 2)(p – 5)
7. (x – 5)(x + 4) 8. (x + 5)(x + 4)
9. (x + 2)(5x + 3) 10. (3x + 2)(x – 4)
11. (2x – 7)(4x – 3) 12. (x +3)(x + 3)
13. (a – 4)(a – 4) 14. (x + 7)(x – 7)
15. (5t + 3)(3t + 2) 16. (2 – x)(3 – x)
17. (3 + p)(5 – p) 18. (4 – 2y)(1 – 3y)
19. (3x + 1)(8 – 2x) 20. (5 – 3x)(2 – 4x)
The quadratic identities
1. Show that (a + b)(a + b) = a 2 + 2ab + b 2 .
The product (a + b)(a + b) can be written as (a + b) 2 . Thus,
(a + b) 2 = (a + b)(a + b)
= a 2 + ab + ab + b 2
= a 2 + 2ab + b 2
This product is illustrated in the figure below.
Consider a square with side (a + b) units. The square is divided into:
(a) square A of side a,
(b) square D of side b,
(c) rectangle B of sides a and b,
(d) rectangle C of sides a and b.
Area of the big square = (a + b) 2
Area of: square A = a 2
rectangle B = ab
rectangle C = ab
square D = b 2
Rectangles B and C are identical.
The area of A + B + C + D = a 2 + ab + ab + b 2
Therefore, (a + b) 2 = a 2 + ab + ab + b 2
= a 2 + 2ab + b 2