Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
222801	Simplify	4p(q-1)+q(1-p)	$4 p (q - 1) + q (1 - p)$
222802	Divide Using Synthetic Division	Use synthetic division to find the result when 3x^3+4x^2-5x-2 is divided by x+2	Use synthetic division to find the result when $3 x^{3} + 4 x^{2} - 5 x - 2$ is divided by $x + 2$
222803	Divide Using Synthetic Division	Use synthetic division to find the result when 3x^3+11x^2-18x+10 is divided by x+5	Use synthetic division to find the result when $3 x^{3} + 11 x^{2} - 18 x + 10$ is divided by $x + 5$
222804	Find the Inverse	y=(1- square root of x)/(1+ square root of x)	$y = \frac{1 - \sqrt{x}}{1 + \sqrt{x}}$
222805	Evaluate	((3x^(3/2)y^3)/(x^2y^(-1/2)))^-2	${(\frac{3 x^{\frac{3}{2}} y^{3}}{x^{2} y^{- \frac{1}{2}}})}^{- 2}$
222806	Solve the Rational Equation for x	-2/(x(x+2))=(x+3)/(x+2)	$- \frac{2}{x (x + 2)} = \frac{x + 3}{x + 2}$
222807	Solve the Inequality for x	-2x^2+2<=x+1	$- 2 x^{2} + 2 \leq x + 1$
222808	Solve the Inequality for y	1>=(-y)/4	$1 \geq \frac{- y}{4}$
222809	Solve the Rational Equation for x	5 square root of x+2=12	$5 \sqrt{x} + 2 = 12$
222810	Evaluate	28 root of 1/(p^6*p)	$\sqrt[28]{\frac{1}{p^{6} \cdot p}}$
222811	Convert to Interval Notation	x<1 and x>-2	$x < 1$ and $x > - 2$
222812	Solve the Rational Equation for x	2/(x-3)+1/x=(x-1)/(x-3)	$\frac{2}{x - 3} + \frac{1}{x} = \frac{x - 1}{x - 3}$
222813	Find the Roots (Zeros)	x^5-3x^4-8x^3-8x^2-9x-5=0	$x^{5} - 3 x^{4} - 8 x^{3} - 8 x^{2} - 9 x - 5 = 0$
222814	Simplify	(a+b)(b+c)(c+a)	$(a + b) (b + c) (c + a)$
222815	Find the Exact Value	sin(pi/6)cos(pi/3)-tan(pi/4)	$\sin (\frac{π}{6}) \cos (\frac{π}{3}) - \tan (\frac{π}{4})$
222816	Solve for x	40/(3x^(1/3))-(5x^(2/3))/3=0	$\frac{40}{3 x^{\frac{1}{3}}} - \frac{5 x^{\frac{2}{3}}}{3} = 0$
222817	Solve for x	x/2+x=9/4	$\frac{x}{2} + x = \frac{9}{4}$
222818	Convert to Interval Notation	x^2<2x+8	$x^{2} < 2 x + 8$
222819	Solve for d	3\|d-4\|>=12	$3 \| d - 4 \| \geq 12$
222820	Find the Intersection	y>=4x-5	$y \geq 4 x - 5$
222821	Find the x and y Intercepts	f(x)=3(x^2+16)(x-6)(x-6)(3x+2)	$f (x) = 3 (x^{2} + 16) (x - 6) (x - 6) (3 x + 2)$
222822	Solve for d	d+10 3/4=-56 1/2	$d + 10 \frac{3}{4} = - 56 \frac{1}{2}$
222823	Simplify	(i^5i^2i^8)^0	${(i^{5} \cdot i^{2} \cdot i^{8})}^{0}$
222824	Solve the Inequality for x	-5\|x-4\|>-20	$- 5 \| x - 4 \| > - 20$
222825	Solve the Inequality for x	-6x^2+9x<=-2x-2	$- 6 x^{2} + 9 x \leq - 2 x - 2$
222826	Evaluate	(15a^0b^2c^34)(3a^16b^-29c^0)	$(15 a^{0} b^{2} c^{34}) (3 a^{16} b^{- 29} c^{0})$
222827	Solve for x	(x-1)^(-4/3)=1/81	${(x - 1)}^{- \frac{4}{3}} = \frac{1}{81}$
222828	Evaluate Using the Given Value	p^2q^2+pq-q^3-p^3 for p=0.5 and q=-0.5	$p^{2} q^{2} + p q - q^{3} - p^{3}$ for $p = 0.5$ and $q = - 0.5$
222829	Simplify	( cube root of 2v^5)( cube root of 18v^6)	$(\sqrt[3]{2 v^{5}}) (\sqrt[3]{18 v^{6}})$
222830	Rationalize the Denominator	5/(-4- square root of 6)	$\frac{5}{- 4 - \sqrt{6}}$
222831	Write the Fraction in Simplest Form	(-6)^-1	${(- 6)}^{- 1}$
222832	Subtract	1/(x-1)-7/(x^2+5x-6)	$\frac{1}{x - 1} - \frac{7}{x^{2} + 5 x - 6}$
222833	Simplify	square root of 24* square root of 80/192	$\sqrt{24} \cdot \sqrt{\frac{80}{192}}$
222834	Simplify the Radical Expression	fourth root of 2* sixth root of 2^5	$\sqrt[4]{2} \cdot \sqrt[6]{2^{5}}$
222835	Write with Rational (Fractional) Exponents	( square root of x^12)/( square root of x^5)	$\frac{\sqrt{x^{12}}}{\sqrt{x^{5}}}$
222836	Divide Using Long Polynomial Division	12x^3+7x^2+9x+2 divided by 4x+1	$12 x^{3} + 7 x^{2} + 9 x + 2$ divided by $4 x + 1$
222837	Evaluate	((8x^11y^-3)/(4x^5y^-7))^0	${(\frac{8 x^{11} y^{- 3}}{4 x^{5} y^{- 7}})}^{0}$
222838	Simplify	-i^6i^3i^5	$- i^{6} \cdot i^{3} \cdot i^{5}$
222839	Evaluate	-7 5/6+(-7 1/4)	$- 7 \frac{5}{6} + (- 7 \frac{1}{4})$
222840	Solve for w	1/6w+1/8=1/3	$\frac{1}{6} w + \frac{1}{8} = \frac{1}{3}$
222841	Evaluate	(11x^3)/(7x^(7/3))	$\frac{11 x^{3}}{7 x^{\frac{7}{3}}}$
222842	Simplify	(5x+10)/(4x-8)*(4-2x)/(x+2)	$\frac{5 x + 10}{4 x - 8} \cdot \frac{4 - 2 x}{x + 2}$
222843	Multiply	33/10*14/22	$\frac{33}{10} \cdot \frac{14}{22}$
222844	Simplify	((x+2)^5-32)/x	$\frac{{(x + 2)}^{5} - 32}{x}$
222845	Simplify/Condense	1/2 log base 3 of x-2 log base 3 of y+4 log base 3 of z	$\frac{1}{2} \log_{3} (x) - 2 \log_{3} (y) + 4 \log_{3} (z)$
222846	Solve by Substitution	-5x+y=-2 and -3x+6y=-12	$- 5 x + y = - 2$ and $- 3 x + 6 y = - 12$
222847	Factor	sec(x)^2-sec(x)-2	$\sec^{2} (x) - \sec (x) - 2$
222848	Solve for x	2^(-3x)*2^(2x)=2^(2x)	$2^{- 3 x} \cdot 2^{2 x} = 2^{2 x}$
222849	Subtract	(2x^2)/7-(8x^5+5x^2y^2)/(x^3+4y^2)	$\frac{2 x^{2}}{7} - \frac{8 x^{5} + 5 x^{2} y^{2}}{x^{3} + 4 y^{2}}$
222850	Find the Excluded Values	(x+2)/(x^2-2x-15)+x/(x+3)	$\frac{x + 2}{x^{2} - 2 x - 15} + \frac{x}{x + 3}$
222851	Factor by Grouping	2ab-3b^2	$2 a b - 3 b^{2}$
222852	Write in Standard Form	(12+8x^3+3x-4x^2)+(5x^3+15-x+2x^2)	$(12 + 8 x^{3} + 3 x - 4 x^{2}) + (5 x^{3} + 15 - x + 2 x^{2})$
222853	Simplify	( fourth root of x* fourth root of 81x)/( fourth root of 16x^36)	$\frac{\sqrt[4]{x} \cdot \sqrt[4]{81 x}}{\sqrt[4]{16 x^{36}}}$
222854	Simplify the Radical Expression	-x square root of 200x^2-9 square root of 2x^4	$- x \sqrt{200 x^{2}} - 9 \sqrt{2 x^{4}}$
222855	Simplify	12g+6f-2f-5g-4f	$12 g + 6 f - 2 f - 5 g - 4 f$
222856	Find the Exact Value	tan(13 degrees )-(sin(13 degrees ))/(cos(13 degrees ))	$\tan (13 °) - \frac{\sin (13 °)}{\cos (13 °)}$
222857	Factor	7x^(5/3)+49x^(2/3)	$7 x^{\frac{5}{3}} + 49 x^{\frac{2}{3}}$
222858	Solve the Rational Equation for x	9+3/(x+3)=-x/(x+3)	$9 + \frac{3}{x + 3} = - \frac{x}{x + 3}$
222859	Simplify	((a^2+3)^(1/3))/((a^2-3)^(-1/3))	$\frac{{(a^{2} + 3)}^{\frac{1}{3}}}{{(a^{2} - 3)}^{\frac{- 1}{3}}}$
222860	Find the Holes in the Graph	f(x)=(2x^2-2x-24)/(x^2+3x)	$f (x) = \frac{2 x^{2} - 2 x - 24}{x^{2} + 3 x}$
222861	Solve for r	v=1/3hpir^2	$v = \frac{1}{3} h π r^{2}$
222862	Solve the Rational Equation for x	3^(x+1)+3^x=12	$3^{x + 1} + 3^{x} = 12$
222863	Simplify the Radical Expression	15 root of x^10b^15	$\sqrt[15]{x^{10} b^{15}}$
222864	Simplify	square root of -6* square root of -2* square root of -5	$\sqrt{- 6} \cdot \sqrt{- 2} \cdot \sqrt{- 5}$
222865	Convert to Interval Notation	10-4\|9y-10\|<-94	$10 - 4 \| 9 y - 10 \| < - 94$
222866	Solve for a	(ma)/(th)=i+love	$\frac{m a}{t h} = i + l o v e$
222867	Factor	x^2-z^2+y^2-2xy	$x^{2} - z^{2} + y^{2} - 2 x y$
222868	Find f(h(x))	f(x) = square root of x-1 and h(x)=x^2+5	$f (x) = \sqrt{x} - 1$ and $h (x) = x^{2} + 5$
222869	Simplify	( cube root of 625z)( cube root of 40z^6)	$(\sqrt[3]{625 z}) (\sqrt[3]{40 z^{6}})$
222870	Divide Using Synthetic Division	Use synthetic division to find the result when 2x^3+x^2-13x-24 is divided by x-3	Use synthetic division to find the result when $2 x^{3} + x^{2} - 13 x - 24$ is divided by $x - 3$
222871	Simplify	(5/(3x))÷(2/(5x^3))	$\frac{5}{3 x} \div \frac{2}{5 x^{3}}$
222872	Simplify	3m^2-3/4(8m-12)+3m	$3 m^{2} - \frac{3}{4} (8 m - 12) + 3 m$
222873	Graph	x-3y=-15 x=-3	$x - 3 y = - 15$ $x = - 3$
222874	Evaluate	-11 2/3*(-4 1/5)	$- 11 \frac{2}{3} \times (- 4 \frac{1}{5})$
222875	Evaluate	((2^3)^10*2^-8)/(2^-7)	$\frac{{(2^{3})}^{10} \cdot 2^{- 8}}{2^{- 7}}$
222876	Simplify	1/2+1/3-1/4	$\frac{1}{2} + \frac{1}{3} - \frac{1}{4}$
222877	Evaluate the Function	f(8) = cube root of 8-9	$f (8) = \sqrt[3]{8 - 9}$
222878	Evaluate	1/e-1	$\frac{1}{e} - 1$
222879	Simplify	square root of 50+3 cube root of 16-5 cube root of 54	$\sqrt{50} + 3 \sqrt[3]{16} - 5 \sqrt[3]{54}$
222880	Solve for x	(3x+4)/(3x)-3=-4/3	$\frac{3 x + 4}{3 x} - 3 = \frac{- 4}{3}$
222881	Expand Using the Binomial Theorem	3(a-4b)^2	$3 {(a - 4 b)}^{2}$
222882	Graph	x+y=-6 y=x	$x + y = - 6$ $y = x$
222883	Solve the Inequality for x	10<-5(x-1)	$10 < - 5 (x - 1)$
222884	Identify the Sequence	2 , 4 , 8 ; dots	$2$ , $4$ , $8$ ; dots
222885	Find the Exact Value	arcsin(sec(0))	$\arcsin (\sec (0))$
222886	Evaluate	-558sin(186)(0.002)sin(186)(0.002)+558cos(186)(0.002)cos(186)(0.002)	$- 558 \sin (186) (0.002) \sin (186) (0.002) + 558 \cos (186) (0.002) \cos (186) (0.002)$
222887	Solve for t	5t+3=4w(t+2)	$5 t + 3 = 4 w (t + 2)$
222888	Simplify	(x+2y-2z)-(2x-5y-6z)	$(x + 2 y - 2 z) - (2 x - 5 y - 6 z)$
222889	Find the Quadratic Equation Given the Roots	0 , -4 , square root of 3	$0$ , $- 4$ , $\sqrt{3}$
222890	Find All Complex Solutions	(10x+25)/(3x+12)=(5x)/(x+4)	$\frac{10 x + 25}{3 x + 12} = \frac{5 x}{x + 4}$
222891	Evaluate	i^6i^25i^19*i^16	$i^{6} \cdot i^{25} \cdot i^{19} \cdot i^{16}$
222892	Multiply	(3 square root of x- square root of 2)^2	${(3 \sqrt{x} - \sqrt{2})}^{2}$
222893	Simplify	((4/3)^2x)^1	${({(\frac{4}{3})}^{2} x)}^{1}$
222894	Evaluate	(6x^3+29x^2+23x-34)(x+3)^-1	$(6 x^{3} + 29 x^{2} + 23 x - 34) {(x + 3)}^{- 1}$
222895	Combine Like Terms	-5y+3y^2+2y-2y^2-9	$- 5 y + 3 y^{2} + 2 y - 2 y^{2} - 9$
222896	Solve the Inequality for x	x-2<x+3	$x - 2 < x + 3$
222897	Solve by Substitution	x-2y=-1 3y=x+4	$x - 2 y = - 1$ $3 y = x + 4$
222898	Find the Parabola with Vertex (0,0) and Directrix y=-2	Vertex (0,0) ; directrix y=-2	Vertex $(0, 0)$ ; directrix $y = - 2$
222899	Simplify	6/(6k-9)-6/2	$\frac{6}{6 k - 9} - \frac{6}{2}$
222900	Solve for w	(7w-10)+4=0	$(7 w - 10) + 4 = 0$