Manual of AlgebraBarnes, 1875 - 331 páginas |
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Página 46
... Find the square of 8ab + 4cd . Ans . 7. Find the square of 2ac - 64a2b2 + 64abcd + 16c2ď3 . 3d . Ans . 4a2c2 12acd + 9d2 . 8. Find the square of 16xy - 7y2 . ― Ans . 256x2y2-224xy3 + 49y . 9. Find the square of 2ab cd . ― Ans 46 MANUAL OF ...
... Find the square of 8ab + 4cd . Ans . 7. Find the square of 2ac - 64a2b2 + 64abcd + 16c2ď3 . 3d . Ans . 4a2c2 12acd + 9d2 . 8. Find the square of 16xy - 7y2 . ― Ans . 256x2y2-224xy3 + 49y . 9. Find the square of 2ab cd . ― Ans 46 MANUAL OF ...
Página 47
William Guy Peck. 9. Find the square of 2ab cd . ― Ans . 4a2b2 4abcd + c2d2 . - 10. Find the product of 2a + 3x , and 2a - 3x . Ans . 4a2 9x2 . 11. Find the product of 7b + 4c , and 7b4c . Ans . 4962 12. Find the product of 8xy + 3x2 ...
William Guy Peck. 9. Find the square of 2ab cd . ― Ans . 4a2b2 4abcd + c2d2 . - 10. Find the product of 2a + 3x , and 2a - 3x . Ans . 4a2 9x2 . 11. Find the product of 7b + 4c , and 7b4c . Ans . 4962 12. Find the product of 8xy + 3x2 ...
Página 128
William Guy Peck. Demonstration of Rule . 95. Let it be required to find the third power of 7ax : from the definition of a ... square is positive , its cube negative , its fourth power positive , and so on . In general , even powers of a ...
William Guy Peck. Demonstration of Rule . 95. Let it be required to find the third power of 7ax : from the definition of a ... square is positive , its cube negative , its fourth power positive , and so on . In general , even powers of a ...
Página 130
... find the square of 3a ̄x ̄ , and that power of 2ax , whose exponent is 3 : it has been shown that any factor may be changed from the denominator to the numerator , or from the numerator to the denominator , by changing the sign of its ...
... find the square of 3a ̄x ̄ , and that power of 2ax , whose exponent is 3 : it has been shown that any factor may be changed from the denominator to the numerator , or from the numerator to the denominator , by changing the sign of its ...
Página 139
... Find the cube of 3a + 2b . OPERATION . Coefficients ; 1 +3 +3 +1 Powers of 3a ; 27a3 + 9a2 + 3a +1 Powers of 2b ; 1 +26 +462 +863 .. ( 3a + 2b ) s = 27a3 + 54a2b + 36ab2 + 8b3 13. Find the square of 7x - 3y . Coefficients ; OPERATION ...
... Find the cube of 3a + 2b . OPERATION . Coefficients ; 1 +3 +3 +1 Powers of 3a ; 27a3 + 9a2 + 3a +1 Powers of 2b ; 1 +26 +462 +863 .. ( 3a + 2b ) s = 27a3 + 54a2b + 36ab2 + 8b3 13. Find the square of 7x - 3y . Coefficients ; OPERATION ...
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Términos y frases comunes
algebraic Arithmetic ax² binomial formula called clearing of fractions coefficients common difference contain contrary signs cube root Davies denominator denote the number distance dividend divisible equa equal roots equation whose roots EXAMPLES exponent expression extracting the square factors Find the cube Find the greatest Find the least Find the square Find the sum following principle following rule geometrical geometrical progression given equation greatest common divisor hence imaginary indicated irreducible fraction least common multiple logarithm Mathematics miles minuend monomial multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quan quotient radical sign ratio real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root Sturm's Theorem substituting subtract third tion tity transposing travels unknown quantity V₁ whole number
Pasajes populares
Página 145 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Página 239 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Página 267 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 245 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 42 - ... the first term of the quotient ; multiply the divisor by this term and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Página 239 - In any proportion, the product of the means is equal to the product of the extremes.
Página 245 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
Página 41 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 264 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.