University Algebra: Embracing a Logical Development of the Science with Numerous Graded ExamplesA.S. Barnes, 1889 - 320 páginas |
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Página 120
... cube negative , its fourth power positive , and so on . In general , any even power of a negative quantity is posi ... find the third power of Za2x 3by From the definition of a power , and the rule 120 ELEMENTS OF ALGEBRA . Powers of ...
... cube negative , its fourth power positive , and so on . In general , any even power of a negative quantity is posi ... find the third power of Za2x 3by From the definition of a power , and the rule 120 ELEMENTS OF ALGEBRA . Powers of ...
Página 129
... Find the 10. Find the sixth power of c Ans . c66c5d + 15c + d2 . - d - - b5 . 20cd3 + 15c2d1 — 6cd5 + de . - It is ... cube of 2a + 3b . Here , 2a takes the place of x in the formula , 36 the place of y , and 3 the place of n , giving ...
... Find the 10. Find the sixth power of c Ans . c66c5d + 15c + d2 . - d - - b5 . 20cd3 + 15c2d1 — 6cd5 + de . - It is ... cube of 2a + 3b . Here , 2a takes the place of x in the formula , 36 the place of y , and 3 the place of n , giving ...
Página 130
... Find the square of 7x -- 3y . OPERATION . 1 + 2 +1 49x2 + 7x + 1 Coefficients . Powers of 7x 1 - 3y + 9y2 Powers of 3y · ( 7x - 3y ) 2 = 49.x2 42xy + 9y2 14. Find the cube of 2x - 3y . OPERATION 130 ELEMENTS OF ALGEBRA .
... Find the square of 7x -- 3y . OPERATION . 1 + 2 +1 49x2 + 7x + 1 Coefficients . Powers of 7x 1 - 3y + 9y2 Powers of 3y · ( 7x - 3y ) 2 = 49.x2 42xy + 9y2 14. Find the cube of 2x - 3y . OPERATION 130 ELEMENTS OF ALGEBRA .
Página 131
... Find the cube of 2x - 3y . OPERATION . 1 + 3 +3 + 1 8x3 + 4x2 + 2x + 1 1 - Coefficients . Powers of 2x . - 3y + 972-27y3 Powers of — 34 ( 2x - 3y ) 3 = 8x3 — 36x2y + 54xу2 — 27y3 -- · 15. Find the cube of + sy . - OPERATION . 1 +3 +3 +1 ...
... Find the cube of 2x - 3y . OPERATION . 1 + 3 +3 + 1 8x3 + 4x2 + 2x + 1 1 - Coefficients . Powers of 2x . - 3y + 972-27y3 Powers of — 34 ( 2x - 3y ) 3 = 8x3 — 36x2y + 54xу2 — 27y3 -- · 15. Find the cube of + sy . - OPERATION . 1 +3 +3 +1 ...
Página 133
... Find the cube of a + ( b + c ) . OPERATION . 1 + 3 + 3 + 1 1 ( a + b + c ) 3 a3 + a2 + a 1 + ( b + c ) + ( b2 + 2bc + c2 ) + ( b3 + 3b2c + 3bc2 + c3 ) a3 + 3a2b + 3a2c + 3ab2 + 6abc + 3ac2 + b3 + 3b'c 2. Find the square of ( 2a — x ) + ...
... Find the cube of a + ( b + c ) . OPERATION . 1 + 3 + 3 + 1 1 ( a + b + c ) 3 a3 + a2 + a 1 + ( b + c ) + ( b2 + 2bc + c2 ) + ( b3 + 3b2c + 3bc2 + c3 ) a3 + 3a2b + 3a2c + 3ab2 + 6abc + 3ac2 + b3 + 3b'c 2. Find the square of ( 2a — x ) + ...
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Términos y frases comunes
algebraic Arithmetic ax² Binomial Formula Clearing of fractions coefficients common difference containing contrary signs cube root Davies denominator denote the number distance dividend divisible equal roots equation whose roots EXAMPLES exponent expressions Extract the square factors Find the cube Find the fourth Find the greatest Find the square following RULE geometrical progression given equation greatest common divisor Hence imaginary indicated irreducible fraction last term least common multiple Let x denote logarithm miles monomial Multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quotient radical sign real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root STURM'S THEOREM Substituting subtract third Transform the equation Transposing travels unknown quantity Whence whole number write X₁
Pasajes populares
Página 258 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 255 - 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.
Página 136 - 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 36 - 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 81 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Página 231 - If four quantities are in proportion, they will be in proportion by COMPOSITION...
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.