Microsoft Math Solver
Solve
Practice
Download
Solve
Practice
Topics
Pre-Algebra
Mean
Mode
Greatest Common Factor
Least Common Multiple
Order of Operations
Fractions
Mixed Fractions
Prime Factorization
Exponents
Radicals
Algebra
Combine Like Terms
Solve for a Variable
Factor
Expand
Evaluate Fractions
Linear Equations
Quadratic Equations
Inequalities
Systems of Equations
Matrices
Trigonometry
Simplify
Evaluate
Graphs
Solve Equations
Calculus
Derivatives
Integrals
Limits
Algebra Calculator
Trigonometry Calculator
Calculus Calculator
Matrix Calculator
Download
Topics
Pre-Algebra
Mean
Mode
Greatest Common Factor
Least Common Multiple
Order of Operations
Fractions
Mixed Fractions
Prime Factorization
Exponents
Radicals
Algebra
Combine Like Terms
Solve for a Variable
Factor
Expand
Evaluate Fractions
Linear Equations
Quadratic Equations
Inequalities
Systems of Equations
Matrices
Trigonometry
Simplify
Evaluate
Graphs
Solve Equations
Calculus
Derivatives
Integrals
Limits
Algebra Calculator
Trigonometry Calculator
Calculus Calculator
Matrix Calculator
Solve
algebra
trigonometry
statistics
calculus
matrices
variables
list
Evaluate
-5yx^{4}
−
5
y
x
4
Differentiate w.r.t. x
-20yx^{3}
−
2
0
y
x
3
Quiz
Algebra
5 problems similar to:
- 5 x ^ { 4 } y
−
5
x
4
y
Still have questions?
Ask a tutor instantly - for free
Get Started
Similar Problems from Web Search
What is the coefficient of the term x^4 y^5 in (x+y+2)^{12}?
What is the coefficient of the term
x
4
y
5
in
(
x
+
y
+
2
)
1
2
?
https://math.stackexchange.com/questions/693371/what-is-the-coefficient-of-the-term-x4-y5-in-xy212
You could use the binomial theorem twice. Let [x^{k}] denote the coefficient of x^k from the polynomial P(x)=\sum_{j=0}^{n}a_jx^j, i.e. [x^{k}]P(x)=a_{k}. Now, \begin{eqnarray}[x^4y^5](x+y+2)^{12}&=&[x^4y^5](x+(y+2))^{12}\\&=&[x^4y^5]\sum_{j=0}^{12}\binom{12}{j}x^j(y+2)^{12-j}\\&=&[y^5]\binom{12}{4}(y+2)^{12-4}\\&=&\binom{12}{4}[y^5](y+2)^8\\&=&\binom{12}{4}[y^5]\sum_{j=0}^{8}\binom{8}{j}y^j2^{8-j}\\&=&\binom{12}{4}\binom{8}{5}2^{8-5}\\&=&\frac{12!}{4!8!}\frac{8!}{5!3!}2^3=\frac{12!2^3}{3!4!5!}\end{eqnarray}
You could use the binomial theorem twice. Let
[
x
k
]
denote the coefficient of
x
k
from the polynomial
P
(
x
)
=
∑
j
=
0
n
a
j
x
j
, i.e.
[
x
k
]
P
(
x
)
=
a
k
. Now,
How do you find the coefficient of \displaystyle{a} of the term \displaystyle{a}{x}^{{4}}{y}^{{5}} in the expansion of the binomial \displaystyle{\left({3}{x}-{2}{y}\right)}^{{9}} ?
How do you find the coefficient of
a
of the term
a
x
4
y
5
in the expansion of the binomial
(
3
x
−
2
y
)
9
?
https://socratic.org/questions/how-do-you-find-the-coefficient-of-a-of-the-term-ax-4y-5-in-the-expansion-of-the
\displaystyle{a}={\left(-{326592}\right)} Explanation: Pattern for power 9 as per Pascal's Triangle 1 9 36 84 126 126 84 36 9 1 \displaystyle{a}{x}^{{4}}{y}^{{5}} is the \displaystyle{6}_{{t}}{h} ...
a
=
(
−
3
2
6
5
9
2
)
Explanation: Pattern for power 9 as per Pascal's Triangle 1 9 36 84 126 126 84 36 9 1
a
x
4
y
5
is the
6
t
h
...
x^4y^4
x
4
y
4
http://www.tiger-algebra.com/drill/x~4y~4/
x4y4 Final result : x4y4 Step by step solution : Step 1 :Final result : x4y4 Processing ends successfully
x4y4 Final result : x4y4 Step by step solution : Step 1 :Final result : x4y4 Processing ends successfully
Can both x^2 + y+2 and y^2+4x be squares?
Can both
x
2
+
y
+
2
and
y
2
+
4
x
be squares?
https://math.stackexchange.com/questions/384100/can-both-x2-y2-and-y24x-be-squares
Thanks to Erick Wong for setting me on the right track. Assume for sake of contradiction that x^2+y+2 and y^2+4x are both perfect squares. Then as y is a positive integer, x^2+y+2 \geq (x+1)^2=x^2 +2x+1 ...
Thanks to Erick Wong for setting me on the right track. Assume for sake of contradiction that
x
2
+
y
+
2
and
y
2
+
4
x
are both perfect squares. Then as
y
is a positive integer,
x
2
+
y
+
2
≥
(
x
+
1
)
2
=
x
2
+
2
x
+
1
...
How do you sketch the graph of \displaystyle{y}=-{5}{x}^{{2}} and describe the transformation?
How do you sketch the graph of
y
=
−
5
x
2
and describe the transformation?
https://socratic.org/questions/how-do-you-sketch-the-graph-of-y-5x-2-and-describe-the-transformation
See below :) Explanation: The standard \displaystyle{y}={x}^{{2}} is drawn in blue, the graph of \displaystyle{y}=-{5}{x}^{{2}} is drawn in red. The tranformations, in order are as follows; - ...
See below :) Explanation: The standard
y
=
x
2
is drawn in blue, the graph of
y
=
−
5
x
2
is drawn in red. The tranformations, in order are as follows; - ...
What is the end behaviour of \displaystyle{y}=-{x}^{{4}} ?
What is the end behaviour of
y
=
−
x
4
?
https://socratic.org/questions/58e54adeb72cff279f0d5371
graph{y = -x^4 [-10, 10, -5, 5]} Explanation: The polynomial is of even degree, so the end behaviour will be in the same direction. The leading coefficient is negative, so \displaystyle\lim_{{{x}\to-\infty}}=-\infty ...
graph{y = -x^4 [-10, 10, -5, 5]} Explanation: The polynomial is of even degree, so the end behaviour will be in the same direction. The leading coefficient is negative, so
x
→
−
∞
lim
=
−
∞
...
More Items
Share
Copy
Copied to clipboard
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
x
2
−
4
x
−
5
=
0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
4
sin
θ
cos
θ
=
2
sin
θ
Linear equation
y = 3x + 4
y
=
3
x
+
4
Arithmetic
699 * 533
6
9
9
∗
5
3
3
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
[
2
5
3
4
]
[
2
−
1
0
1
3
5
]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
{
8
x
+
2
y
=
4
6
7
x
+
3
y
=
4
7
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
d
x
d
(
x
−
5
)
(
3
x
2
−
2
)
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
∫
0
1
x
e
−
x
2
d
x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
x
→
−
3
lim
x
2
+
2
x
−
3
x
2
−
9
Back to top