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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.
If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+
48 more than the quotientvof a number and 64
-6x-4y=-6 x+2y=-3
how many times In a 12 hour period will he numbers add up to 6? (hint 3:00 is one answer0
i need help trying make a presentation for my teacher
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Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans: Given : - ∠APB = 120o Construction : -Join OP To prove : -
Inverse Cosine : Now see at inverse cosine. Following is the definition for the inverse cosine. y = cos -1 x ⇔ cos y = x for
1 1/3:2/3:1/6
Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
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