The intermediate step in the work may be omitted, and the products written at once, as in the following examples:
(x + 2) (x+3)=x^2+5x+6. (x— 3) (x+ 4)= x^2+ e— 12. (x+6) (x—9)=x^2 — 3a —54. (x—4y) (x—10y)= x^2 — 14xy + 40y^2. (x— 6y) (x+4y)= x^2 -2xy — 24y^2.
By an easy extension of these principles we may write the product of any two binomials.
Thus (x+3y) (x— y)= x^2 + 3xy —2xy—3y^2 = x^2 + xy — 3y^2. (3x—4y)(2x+y)= 6x^2 —8xy+3xy—4y^2 = 6x^2 — 5xy — 4y^2.
EXAMPLES IV. f.
Write the values of the following products:
1. (x+ 8)(a— 5). 15. (a —6)(a+4 13).
2. (x+6)(x—1). 16. (a+ 8)(a + 8).
8. (x — 3)(a+ 10). 17. (a—11)(x+411). 4. (x—1)(x+ 5). 18. (a —8)(a—8).
5. (x+ 7)(x—9). 19. (x—8a)(x+ 2a). 6. (x—10)(x — 8). 20. (x+ 6a)(x—5a). 4. (x—4)(x+ 11). 21. (x+ 3a)(x- 3a). 8. (x— 2)(x+ 4). 22. (x+ 4y)(x —2y). 9. (x+ 2)(x—2). 23. (x+7y)(x—7y). 10. (a—1)(a +1). 24. (x—3y)(x— 3y). 11. (a+9)(a—5). 25. (3x—1)(x+1).
12. (a — 8)(a + 12). 26. (2x+5)(2x—1). 13. (a-8)(a +4) 27. (3x+ 7) (2x —3). 14. (a—8)(a +8). 28. (4x —8)(2x+ 3).
