Algebra for Beginners |
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Page 20
... cube of x , − x2 + x - 2x2 , and x3 - x - x2 + 1 . - 20. Take p2 - q2 from 3pq - 4q2 , and add the remainder to the sum of 4pq - p2 - 3q2 and 2p2 + 6q2 . 21. Subtract 363 + 262-8 from zero , and add the result to b4-2b3 + 3b . 22. By ...
... cube of x , − x2 + x - 2x2 , and x3 - x - x2 + 1 . - 20. Take p2 - q2 from 3pq - 4q2 , and add the remainder to the sum of 4pq - p2 - 3q2 and 2p2 + 6q2 . 21. Subtract 363 + 262-8 from zero , and add the result to b4-2b3 + 3b . 22. By ...
Page 44
... cube , fourth , fifth , & c . , root of any expression is that quantity whose third , fourth , fifth , & c . , power is equal to the given expression . The roots are denoted by the symbols 3 / , / , 5 / , & c . Examples . 3/27 = 3 ...
... cube , fourth , fifth , & c . , root of any expression is that quantity whose third , fourth , fifth , & c . , power is equal to the given expression . The roots are denoted by the symbols 3 / , / , 5 / , & c . Examples . 3/27 = 3 ...
Page 84
... 2y + 7-2-2 4 - | y ) 13. 7 + y - 22 = X 14 . 15 . 3 } { ( x + y ) = = y - x = x - z = z − 3 . = y + 2 = x + y + z + 2 = 0 . -y + 22 - y - z - 2 3 - Example 2. Find the cube root of 8x6 - 48x 84 [ CHAP . XIII . ALGEBRA .
... 2y + 7-2-2 4 - | y ) 13. 7 + y - 22 = X 14 . 15 . 3 } { ( x + y ) = = y - x = x - z = z − 3 . = y + 2 = x + y + z + 2 = 0 . -y + 22 - y - z - 2 3 - Example 2. Find the cube root of 8x6 - 48x 84 [ CHAP . XIII . ALGEBRA .
Page 89
... cube of any binomial ; ( 3 ) the square of any multinomial . 113. It is evident from the Rule of Signs that ( 1 ) no even power of any quantity can be negative ; ( 2 ) any odd power of a quantity will have the same sign as the quantity ...
... cube of any binomial ; ( 3 ) the square of any multinomial . 113. It is evident from the Rule of Signs that ( 1 ) no even power of any quantity can be negative ; ( 2 ) any odd power of a quantity will have the same sign as the quantity ...
Page 90
... cube of each of the following expressions : 17. 2x . 18. 3ab2 . 19 . 4x3 . 20 . -3a2b . 21. - 4x3y2 . 22. -b2cd3 . 23 . - 6y . 24 . - 4p3q3 . 1 2 3x2 25 . 26 . 27 . P + p3 ° ab2c3 28. -23 . 4y23 Write down the value of each of the ...
... cube of each of the following expressions : 17. 2x . 18. 3ab2 . 19 . 4x3 . 20 . -3a2b . 21. - 4x3y2 . 22. -b2cd3 . 23 . - 6y . 24 . - 4p3q3 . 1 2 3x2 25 . 26 . 27 . P + p3 ° ab2c3 28. -23 . 4y23 Write down the value of each of the ...
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Common terms and phrases
A's age a²+b² acres algebraical sum Arithmetic arranged B's age beginner binomial cents CHAPTER coefficient Completing the square compound expressions contains convenient descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII Find the highest Find the lowest find the number Find the product Find the square Find the sum find the value following expressions given expressions half-dollars Hence highest common factor lowest common denominator lowest common multiple lowest terms miles an hour miles per hour minute-hand Multiply negative numerator and denominator obtain quadratic equation quotient Reduce to lowest remainder removing brackets Resolve into factors result rule of signs side simple equation Simplify simultaneous equations Solve the equations square root subtract Transposing trinomial unknown quantities walk whence write yards
Popular passages
Page 160 - An equation which contains the square of the unknown quantity, but no higher power, is called a quadratic equation, or an equation of the second degree. If the equation contains both the square and the first power of the unknown, it is called...
Page 188 - Elementary Trigonometry" etc Edited mi*l Arranged for American Schools By CHARLOTTE ANGAS SCOTT, D.SC., Head of Math. Deft., Bryn Mauir College, Pa. 1 6mo. Cloth. 75 cents. " Evidently the work of a thoroughly good teacher. The elementary truth, that arithmetic is common sense, is the principle which pervades the whole book, and no process, however simple, is deemed unworthy of clear explanation. Where it seems advantageous, a rule is given after the explanation. . . . Mr. Lock's admirable Trigonometry...
Page 105 - Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Page 89 - The product is a2+2a6-}-62; from which it appears, that the square of the sum of two quantities, is equal to the square of the first plus twice the product of the first by the second, plus the square of the second.
Page 87 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 89 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.