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Example 1
Add 4x4 + 3x3 - x2 + x + 6 and -7x4 - 3x3 + 8x2 + 8x - 4
We write them one below the other as shown below.
4x4 + 3x3 - x2 + x + 6
(+)
-7x4 - 3x3 + 8x2 + 8x - 4
-3x4 + 0 + 7x2 + 9x + 2
Example 2
Add 5x5 - 6x3 + 4x2 + 3x - 7, 3x5 - 2x4 + 3x2 + 6x - 1
and- 3x4 + x3 - 5x2 + 7x + 4
5x5 + - 6x3 + 4x2 + 3x - 7
3x5 - 2x4+ + 3x2 + 6x - 1
- 3x4+ x3 - 5x2 + 7x + 4
8x5 - 5x4 - 5x3 + 2x2 + 16x - 4
Example 3
Subtract -7x4 - 3x3+ 8x2 + 8x - 4 from 4x4 + 3x3 - x2 + x + 6
4x4 + 3x3- x2 + x + 6
(-)
11x4 + 6x3 - 9x2 - 7x + 10
In this problem, in some expressions we do not find terms of certain powers. They have been left as blanks.
Example 4
Subtract the first from the second and sum the difference with the third expression. The expressions are given below.
5x5 - 6x3 + 4x2 + 3x - 7, 3x5 - 2x4 + 3x2 + 6x - 1 and -3x4 + x3 - 5x2 + 7x + 4.
The difference of first two expressions is given by
3x5 - 2x4 + 3x2 + 6x - 1
5x5 - 6x3 + 4x2 + 3x - 7
-2x5 - 2x4 + 6x3 - x2 + 3x + 6
The sum of the difference between the first two expressions and the third expression will be as shown below.
(+) - 3x4+ x3 - 5x2 + 7x + 4
-2x5 - 5x4+ 7x3 - 6x2 + 10x + 10
The vector a → =(2,4) compute 3a → , ½ a → and -2a → . Graph all four vectors on similar axis system. Solution: Now here are the three scalar Multiplication 3a → = (6,
If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans: d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,
Oscar's Oil Company provides customers a 5% discount if they pay their bill within 10 days. The Stevens' oil bill is $178. How much do they save if they pay the bill inside 10 days
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sin(2x+x)=sin2x.cosx+cos2x.sinx =2sinxcosx.cosx+(-2sin^2x)sinx =2sinxcos^2+sinx-2sin^3x =sinx(2cos^2x+1)-2sin^3x =sinx(2-2sin^2x+1)-2sin^3
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
FORMULAS DERIVATION
how many mg are there in g?
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