ALGEBRA - solved problems
 Solutions: a)  2a2 + 5a - a2 - a = a2 + 4a,       b)  3a4 - 7a4 + a4 = (3 - 7 + 1) · a4  = -3a4
Only the same powers (with same base and the exponent) can be added or subtracted.
We also say that only like or similar terms can be added. The number that multiply the power is called coefficient. We add or subtract the same powers by adding or subtracting their coefficients.
The rules for powers (or exponents)
 Rules Examples am · an  = am + n, a)  a3 · a4 = a3 + 4,                 b)  24 · 25 = 24 + 5 = 29 = 512, am ¸ an  = am - n, a)  x5 ¸ x3  = x5 - 3  = x2,       b)  0.14 ¸ 0.13 = 0.14 - 3 = 0.1, an · bn  = (a · b)n, a)  24 · 34 = (2 · 3)4 = 64,        b)  45 · 0.85 = (4 · 0.8)5 = 3.25, an ¸ bn  = (a ¸ b)n, a)  x6 ¸ y6  = (x ¸ y)6,             b)  125 ¸ 35 = (12 ¸ 3)5 = 45,  (am)n  = am · n, a)  (a3)4 = a3 · 4 = a12,             b)  (45)3 = 45 · 3 = 415,      Simplifying an exponential expression
 61 Simplify given expressions.
 Solutions:   Scientific notation
 62 Write in scientific notation and vice versa.
 Solutions: a)  0.0000007054 = 7.054 · 10-7,         b)  5.2 · 10-4 = 0.00052
 c)  4507000000 = 4.507 · 109,             d)  1.04 · 105 = 104000
A number in scientific notation is written as the product of a number called coefficient and a power of 10.
While converting to scientific notation, the decimal point of the coefficient is placed behind the first non-zero digit. The sign of the exponent of the power indicates, how many places the decimal point was moved to the right or to the left. Quadratic equation  x2 = aa > 0
 Solutions: a)   x2 = 16 b)   (x - 5)2 = 49 x2 - 42 = 0 (x - 5)2 - 72 = 0 (x - 4) · (x + 4) = 0 [(x - 5) - 7] · [(x - 5) + 7] = 0 x - 4 = 0    =>   x1 = 4 (x - 5) - 7 = 0    =>   x1 = 12 x + 4 = 0    =>   x2 = - 4 (x - 5) + 7 = 0    =>   x2 = -2
 Solutions:  Square root
Properties of square roots
 Properties Examples              Adding, subtracting, multiplying and dividing square roots
 65 Solve given square roots operations.
 Solutions:      Rationalizing a denominator
 66 Eliminate radicals from denominators of fractions .
 Solutions:      Solved problems contents 