How can I simplify these expressions?
(I) (2x + 3a)(3x +2a) - 2(x+2a)(x-a)= [6x^2 + 6xa + 9xa +6a^2] - 2[x^2 - xa +2xa - 2a^2]= 4x^2 +11xa +10a^2(II) x^2(1+1/x)^2= x^2[(1) + (2/x )+(1/(x^2))]=x^2 + 2x + 1
How do you simplify this radical expression?
cuberoot 4 + cuberoot 32 =Simplify cuberoot 32cuberoot 4 + cuberoot (8 x 4) =Take the cuberoot of 8cuberoot 4 + 2cuberoot 4 =Add like terms3cuberoot 4 ANSWER
2/3(3x - 15y) + (9y - 11x) simplify the expression for me please?
2/3(3x - 15y) + (9y - 11x) 6x/3 - 30y/3 + 9y -11x 2x - 10y +9y - 11x -9x -y
Help me simplify this expression please?
e^(2lnx+3lny)/x*y e^(ln x^2 + ln y^3)/(x*y) I assume this is what is on the bottom. Strict precedence is different. e^ln(x^2 * y^3)/(xy) (x^2*y^3)/(xy) x*y^2
Please help me simplify this expression!?
((3a^-6)/(3b^-1/3))^-1=[(3b^1/3)/3a^6)]^... = (b^1/3/a^6)^-1 =a^6/b^1/3
What does it mean to simplify an expression?
In short, it means finding the simplest expression (or in many cases just a simpler one) that is equivalent to the initial one.But, it is actually quite hard to precisely define what simplifying an expression means. The first reason is that what is simpler can be highly subjective. For example, you can write [math]x^{\frac12}[/math] or [math]\sqrt{x}[/math], which for me are both equally simple, but some may disagree.But let's say that we have some well-defined metric of "simplicity", for example, we can say that the simplest expression is the one with the fewest symbols. This is well-defined and if we have a finite number of symbols, we can theoretically always find the simplest one by manually checking all strings of symbols that are shorter than the initial expression and checking if they are equivalent. The second problem is ascertaining what the term equivalent means for expressions. If expression does not contain any free variables, for example [math]1 + 2 + 3 + 4[/math], it is equivalent, if it evaluates to the same number, or whatever other object the expression represents (matrices, group elements, ...). But if the expression contains free variables, such as [math]1 + x^2[/math], then the expression is actually an implicit definition of a function. In this case, two expressions are equivalent if and only if they define the same function. Two functions are equal ifThey have the same domain (= are defined on the same set)They map to the same value for every value of the domain.So, technically [math]1 + x^2[/math] and [math]1 + \frac{x^3}{x}[/math] are not equivalent, since the latter defines a function which is not defined on [math]x = 0[/math]. In practice we often ignore such cases, though.The problem of equivalence is also that there is no practical general algorithm for checking for equivalence of expressions. If such an algorithm existed, it would contradict the halting problem, and would allow us to prove every statement in mathematics by expressing it as an expression and checking that it is equivalent to a tautology. Therefore, in practice, expressions are simplified by pattern matching and replacement . For example, we have two replacement rules [math]\square \mapsto 1\square[/math], [math]m\square + n\square \mapsto [m + n]\square[/math] and repeatedly applying those would transform [math]x + x + x + x[/math] to [math]4x[/math].
How can I simplify the Boolean expression "A’C+AB+AB’C+BC"?
If we recognize that A + A’ = 1 and AB’ + B = A + B (absorption)Then A’C + AB + AB’C + BC= C (A’ + AB’ + B) + AB (distributive property)= C (A’ + A + B ) + AB= C ( 1 + B) + AB= C + AB
Can anyone help me simplify this expression 2a^2b+2b^2-3ab-4(ab-b^2)?
2a^2b + 2b^2 - 3ab - 4(ab-b^2) = 2a^2b + 2b^2 - 3ab - 4ab - 4b^2 = 2a^2b - 2b^2 - 7ab
Can someone show me how to simplify this expression
(z^10/32)^4/5 =Property of exponents: (a/b)^n = a^n/b^n[(z^10)^4/5]/(32^4/5) =Same property of exponents(z^8)/(2^4) = Simplify denominator. (z^8)/16. ANSWER