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Example
Multiply 3x5 + 4x3 + 2x - 1 and x4 + 2x2 + 4.
The product is given by
3x5 . (x4 + 2x2 + 4) + 4x3. (x4 + 2x2 + 4) + 2x .
(x4 + 2x2 + 4) - 1 . (x4 + 2x2 + 4)
= 3x5 . x4 + 3x5 . 2x2 + 3x5 . 4 + 4x3 . x4 + 4x3 .
2x2 + 4x3 . 4 + 2x . x4 + 2x . 2x2 + 2x . 4 - x4 - 2x2 - 4
To simplify the above we employ a rule which we will learn in laws of indices. It states that xm . xn = xm+n
= 3x9 + 6x7 + 12x5 + 4x7 + 8x5 + 16x3 + 2x5 + 4x3 + 8x - x4 - 2x2 - 4
Now we collect like terms and simplify them. We obtain 3x9 + 10x7 + 22x5 - x4 + 20x3 - 2x2 + 8x - 4.
Find out the domain of each of the following. (a) f (x,y) = √ (x+y) (b) f (x,y) = √x+√y (c) f (x,y) = ln (9 - x 2 - 9y 2 ) Solution (a) In this example we know
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Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
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