Explanation (x −y)3 = (x − y)(x −y)(x −y) Expand the first two brackets (x −y)(x − y) = x2 −xy −xy y2 ⇒ x2 y2 − 2xy Multiply the result by the last two brackets (x2 y2 −2xy)(x − y) = x3 − x2y xy2 − y3 −2x2y 2xy2 ⇒ x3 −y3 − 3x2y 3xy2 Always expand each term in the bracket by all the other How do you simplify #(x^5y^8)/(x^4y^2)#?Simplify xyz xyz' x'yz' x'y'z Step 1 Draw the Karnaugh that represents the expression by carefully a mark in each appropriate square Cover the marked boxes as best you can with ovals, using as few rectangles as possible Allowed coverings for this expanded setup is
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(1) "z2" was replaced by "z^2" 2 more similar replacement(s) Step 1 Equation at the end of step 1 (((((2•(x 2))3y)2 2 z 2)3x)5y)z 2 Step 2 Equation at the end of step 2 ((((2x 2 3y) 2 2 z 2) 3x) 5y) z 2 Step 3 Final result 2x 2 3x 2y 3z 2 using identity a 3 b 3 c 3 3abc = (a b c)(a 2 b 2 c 2 – ab – bc – ca) if a b c = 0;X(z) = z z −3 (18) Inserting the second equation into the first gives
No integers x;y;z with xyz6= 0 satisfy x3 y3 z3 = 0 Proof We may assume that x, y, and zare pairwise coprime If xyzis not divisible by 3, then the equation has no solution even in Z=(9), where every nonzero cube is 1 Suppose then, without loss of generality, that 3jz We will work in the UFD R= Z with = ( 1i p 3)=2, a root of the lim x→a−f (x) lim x → a − f ( x) is a left hand limit and requires us to only look at values of x x that are less than a a In other words, we will have lim x→af (x) =L lim x → a f ( x) = L provided f (x) f ( x) approaches L L as we move in towards x =a x = a (without letting x = a x = a) from both sides How do you simplify #(4xy)(2x^4 yz^3 y^4 z^9)#?
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The volume is the integral of the function 1 over the ellipsoid You can evaluate it by changing variables to X = x 2y, Y = x− 2y z, Z = 3 z In the new coordinates, one now has Resolution of the singularities of the curve X^2Y^2 Y^2Z^2 X^2Z^2=0 Resolution of the singularities of the curve X 2Y 2 Y 2Z 2 X 2Z 2 = 0U xx= 6x 6 u y= 6xy 6y;For maximum, x,y and z should be equal to each other (ie x=y=z) so x=y=z=1/3 since xyz=1 (1/3)*(1/3)^3 (1/3)*(1/3)^3 (1/3)*(1/3)^3 = (1/9)^3 (1/9)^3 (1/9)^3 = 3/729 = 1/243 If x,y,z\geq 0 and xyz = 10 , Then Max value of xyzxyyz zx,
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(17x^9)/(yz^2) (8x^3*y^2*z^2)*(3x^2)/(y^3z^4) multiply fractions ((8x^3*y^2*z^2)3x^2)/(y^3*z^4) expand (11x^5*3x^2*y^2*3x^2*z^2)/(y^3*z^4) collect liketerms (17x^9*y^2*z^2)/(y^3*z^4) divide (17x^9)/(y*z^2)Subtract x^ {3} from both sides Subtract x 3 from both sides Combine x^ {3} and x^ {3} to get 0 Combine x 3 and − x 3 to get 0 Reorder the terms Reorder the terms This is true for any x This is true for any x Use the distributive property to multiply xy by x^ {2}xyySimplify (x y) 3 (x y) 3 Simplifying Mathematical Expressions There are a number of different types of mathematical expressions in the study of mathematics
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One Time Payment $1999 USD for 3 months Weekly Subscription $249 USD per week until cancelled Monthly Subscription $799 USD per month until cancelled Annual Subscription $3499 USD per year until cancelledSimplify (xy)^3 (x − y)3 ( x y) 3 Use the Binomial Theorem x3 3x2(−y) 3x(−y)2 (−y)3 x 3 3 x 2 ( y) 3 x ( y) 2 ( y) 3 Simplify each term Tap for more steps Rewrite using the commutative property of multiplication x 3 3 ⋅ − 1 ( x 2 y) 3 x ( − y) 2 ( − y) 3 x 3 3 ⋅ 1 ( x 2 y) 3 x ( y) 2Your answer would be x^4yz/3 If you bring x^1 to the numerator that would be 3x^3 (x^1)y^4z^2/6y^3z^3 so simplified it would be 3x^4y^4z^2/6y^3z^3 Now simplify the z's bring z^3 to the numerator And get 3 x^4 y^4 z^2 (z^3) /6y^3 Simplified is 3x^4 y^4 z/ 6y^3
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Answer 3ab ⋅ 4√b 3 a b ⋅ 4 √ b Example 8 Simplify 5√− 32x3y6z5 5 √ − 32 x 3 y 6 z 5 Solution Notice that the variable factor x cannot be written as a power of 5 and thus will be left inside the radical In addition, for y6 = y5 ⋅ y y 6 = y 5 ⋅ y ;Answer by lenny460 (1073) ( Show Source ) You can put this solution on YOUR website!Get stepbystep solutions from expert tutors as fast as 1530 minutes
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How do you multiply #(3m1)(m4)(m5)#?Calculus Simplify x^3y^3 x−3 − y−3 x 3 y 3 Rewrite the expression using the negative exponent rule b−n = 1 bn b n = 1 b n 1 x3 − y−3 1 x 3 y 3How do you find the volume of a prism if the width is x, height is #2x1# and the length if #3x4#?
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Move y−6 y 6 to the numerator using the negative exponent rule 1 b−n = bn 1 b n = b n Apply the product rule to x3y6 x 3 y 6 Multiply the exponents in (x3)1 3 ( x 3) 1 3 Tap for more steps Apply the power rule and multiply exponents, ( a m) n = a m n ( a m) n = a m n Cancel the common factor of 3 3Solvevariablecom contains valuable facts on solve for y calculator, solving exponential and quadratic function and other algebra subjects In cases where you have to have advice on mixed numbers or even grade math, Solvevariablecom is simply the ideal site to explore!X∞ =3 (1/2)nz−n= X∞ z−1 2 n Letl= n−3 Then X 1(z) = X∞ l=0 z−1 2 l3 = (z−1/2)3 1−(z− 1/2) = 1 8z2(z− 2) TheROCisz>1/2 An alternative approach is to think of x 1n as 1 8 times a version of 1 2 nun that is delayed by 3 The Z transform of 1 2 nun is z z−1 2 Delaying it by 3 multiplies the transformbyz−3
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Expand (xy)^3 (x y)3 ( x y) 3 Use the Binomial Theorem x3 3x2y3xy2 y3 x 3 3 x 2 y 3 x y 2 y 3Since is too small and is too big, one of the numbers (call it y) must be 4 And that leaves , so x=3 In other words, (3,4,5) is the only solution using positive integers, up to permutation If you relax that to allow zero, then (0,0,6) is a solutionAlgebra Factor x^3y^3 x3 − y3 x 3 y 3 Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 abb2) a 3 b 3 = ( a b) ( a 2 a b b 2) where a = x a = x and b = y b = y (x−y)(x2 xyy2) ( x y) ( x 2 x y y 2)
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You can simplify (x y)^3 to either (x y) (x y) (x y) or (x y)^2 (x y) But using those two will result in same answer which will be in this format > 1, 3, 3, 1 Hence rArr (x y)^3 = (x y) (x y) (x y) (x y) (x y) (x y) (x y) (x y) (x y) (x y) x^2 xy xy y^2 This lead to the point using difference of two cubes as (x y) x^2 2xy y^2 x x^2 2xy y^2 y x^2 2xy y^2 x^3 2x^2y xy^2 x^2y 2xy^2 y^3 Collect like terms color(red)(xSimplify Enter expression, eg x^25x6 Sample Problem Factor Enter expression, eg (x1)^3 Sample Problem Expand Enter a set of expressions, eg ab^2,a^2b Ask the user to enter the values of a, b and c and then print out the values of x) Note You can calculate the values by using the quadratic formula and using methods ofClick here to see ALL problems on Linear Algebra Question Simplify ( (3/x) (4/y))/ ( (4/x) (3/y)) Found 2 solutions by radh, MathTherapy Answer by radh (108) ( Show Source ) You can put this solution on YOUR website!
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5 Solution Take the ztransforms of the difference equation and of the input This yields Y(z) −2z−1Y(z) = z−1X(z)−z−2X(z); secutive odd numbers is (iv) The successor of the number 99,99,999 is (v) The largest number formed by the digits 7, 3, 0, 6, 4 and 9 rounded off to the nearest thou is Multiple Choice Questions (MCQs) Tick ( ) the correct option 2 We can use the exponent or product rule for powers (2 and 3) that have the same base (3) in order to multiply similar bases that have their respective powers, add the exponents, which in this case are 2 and 3, viz 3^2 x 3^3 = 3^ (23) = 3^5 3^5 = 3 × 3 × 3 × 3 × 3 = 243 grendeldekt and 4 more users found this answer helpful
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How do you simplify #(2^3 *3^2) / (2^4 * 3^2)^2#?Polynomial Identities When we have a sum (difference) of two or three numbers to power of 2 or 3 and we need to remove the brackets we use polynomial identities (short multiplication formulas) (x y) 2 = x 2 2xy y 2 (x y) 2 = x 2 2xy y 2 Example 1 If x = 10, y = 5a (10 5a) 2 = 10 2 2·10·5a (5a) 2 = 100 100a 25a 2Answer to Simplify x^3 y^4/3y^4 A x/y^8 B 3/x^5 y^3 c 3x^4/4y^4 D x^34/3 Find solutions for your homework or get textbooks Search
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Algebra > Coordinate Systems and Linear Equations > SOLUTION simplify the following expression 3x^3 y^4 z^2 6x^1 y^3 z^3 I don't get how to do it, I've tried everything, Please help Log On(Remember to use the chain rule on D ( y 2/3) ) (2/3)x1/3 (2/3)y1/3 y' = 0 , so that (Now solve for y' ) (2/3)y1/3 y' = (2/3)x1/3, , and , Since lines tangent to the graph will have slope $ 1 $ , set y' = 1 , getting , y 1/3 = x 1/3, y 1/3 = x 1/3, ( y 1/3) 3 = ( x 1/3) 3, or y = x Substitue this into the ORIGINAL equation x 2/3
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