Secondary Algebra

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22. (aj + y + 5)(aj + y-5).
23. (4 a - 3 b - 7) (4 a - 3 b + 7).
24. (^ + / + z 2 )(-* 2 + 2/ 2 + Z 2 )' 25. (a 2 - ab 4- 6 2 ) 2 + 2a;-l)(> 2 -2z-l).
27. (x 4 - x 2 4- 1) (V 4- a^ - 1).
28. (-c^- Simplify the following expressions : 29. (l 30. (2x 31. (a; - 3) (a -1) (a? + !)( + 3).
32. (a x)(a + x) (a 2 + x~) (a 4 33. (aj'- 34. (aj z - 35. (a + & - c) (a + c - 6) (6 + c - a) (a + & -f c).
The Product (x + a) (x + 6) . 7. By actual multiplication, we have (JT + a)(jf + 6) = * 2
... + a* + 6jr + a6 = jr 2 + (a + 6)jr + a^ ; (JT + a)(jr 6) = jr 2 + ajr 6jr ab = x 1 + (a b)x ab ; (JT a)(jr 6) = x 2 ax bx + ab = x 2 (a + 6)jf -f aA.
We thus derive the following method for multiplying two binomials which have a common first term : The first term of the product is the square of the common first terms of the binomials.
6-7] TYPE-FORMS IN MULTIPLICATION 93 The coefficient of the second term of the product is the algebraic sum of the second terms of the binomials.
The last term of the product is the product of the last terms of the binomials.


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