\(x\left(x+y\right)\left(x-y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\)

\(=x\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\)

\(=x\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\)

\(=x\left(x^8-y^8\right)\left(x^8+y^8\right)+xy^{16}\)

\(=x\left(x^{16}-y^{16}\right)+xy^{16}=x^{17}-xy^{16}+xy^{16}=x^{17}\)

  15.82 - 5.100 + 15.18

= (15.82 + 15.18) - 5.100

= 15.(82 +18) - 5.100

= 15.100 - 5.100

= 100.(15 - 5)

= 100.10

= 1000

  {[2.5² + (11 - 8³)] + 2024⁰} : 2

= {2.25 + (11 - 512) + 1} : 2

= {50 - 501+1} : 2

= {- 451 + 1} : 2

= - 450 : 2

= - 225

= - 1 : 2

 = - \(\dfrac{1}{2}\)

Diện tích 1 viên gạch là: \(60\cdot60=3600\left(cm^2\right)=0,36\left(m^2\right)\)

Diện tích căn phòng là \(400\cdot0,36=144\left(m^2\right)\)

Độ dài cạnh của nền căn phòng là:

\(\sqrt{144}=12\left(m\right)\)

\(x^2-4+3\left(x-2\right)=0\)

=>(x-2)(x+2)+3(x-2)=0

=>(x-2)(x+2+3)=0

=>(x-2)(x+5)=0

=>\(\left[{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)

a: 48-3(x+5)=24

=>3(x+5)=48-24=24

=>\(x+5=\dfrac{24}{3}=8\)

=>x=8-5=3

b: \(2^{x+1}-2^x=32\)

=>\(2\cdot2^x-2^x=32\)

=>\(2^x=32=2^5\)

=>x=5

c: \(\left(15+x\right):3=3^3\)

=>\(x+15=3^3\cdot3=3^4=81\)

=>x=81-15=66

d: \(250-10\left(24-3x\right):15=224\)

=>\(\dfrac{2}{3}\left(24-3x\right)=250-224=26\)

=>\(24-3x=26:\dfrac{2}{3}=26\cdot\dfrac{3}{2}=39\)

=>3x=24-39=-15

=>\(x=-\dfrac{15}{3}=-5\)

\(\dfrac{1}{99}-\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-...-\dfrac{1}{3\cdot1}\)

\(=\dfrac{1}{99}-\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{97\cdot99}\right)\)

\(=\dfrac{1}{99}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{99}-\dfrac{1}{2}\left(1-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{99}-\dfrac{1}{2}\cdot\dfrac{98}{99}=\dfrac{1}{99}-\dfrac{49}{99}=-\dfrac{48}{99}=\dfrac{-16}{33}\)

j: \(\left(5^7+7^5\right)\left(6^8+8^6\right)\left(2^4-4^2\right)\)

\(=\left(5^7+7^5\right)\left(6^8+8^6\right)\left(16-16\right)\)

\(=0\cdot\left(5^7+7^5\right)\left(6^8+8^6\right)\)

=0

k: \(\left(7^{50}+7^{29}\right)\left(5^{14}+5^{26}\right)\left(3^{35}\cdot3-9^{18}\right)\)

\(=\left(7^{50}+7^{29}\right)\cdot\left(5^{14}+5^{26}\right)\left(3^{36}-3^{36}\right)\)

\(=\left(7^{50}+7^{29}\right)\left(5^{14}+5^{26}\right)\cdot0=0\)

\(\dfrac{-3}{7}+\left(3-\dfrac{3}{4}\right)-\left(-2,25-\dfrac{10}{7}\right)\)

\(=\dfrac{-3}{7}+\left(3-\dfrac{3}{4}\right)-\left(-\dfrac{9}{4}-\dfrac{10}{7}\right)\)

\(=\dfrac{-3}{7}+\left(\dfrac{12}{4}-\dfrac{3}{4}\right)-\left(-\dfrac{63}{28}-\dfrac{40}{28}\right)\)

\(=\dfrac{-3}{7}+\dfrac{9}{4}-\left(\dfrac{-103}{28}\right)\)

\(=\dfrac{-12}{28}+\dfrac{63}{28}-\left(\dfrac{-103}{28}\right)\)

\(=\dfrac{51}{28}-\left(\dfrac{-103}{28}\right)\)

\(=\dfrac{51}{28}+\dfrac{103}{28}\)

\(=\dfrac{154}{28}\)

\(=\dfrac{11}{2}\)

\(-\dfrac{3}{7}+\left(3-\dfrac{3}{4}\right)-\left(-2,25-\dfrac{10}{7}\right)\)

\(=-\dfrac{3}{7}+3-\dfrac{3}{4}+2,25+\dfrac{10}{7}\)

\(=\left(-\dfrac{3}{7}+\dfrac{10}{7}\right)+\left(3-\dfrac{3}{4}+2,25\right)\)

\(=\left(-\dfrac{3}{7}+\dfrac{10}{7}\right)+\left(\dfrac{12}{4}-\dfrac{3}{4}+\dfrac{9}{4}\right)\)

\(=1+\dfrac{18}{4}\)

\(=\dfrac{22}{4}\)

\(-2,25-\dfrac{10}{7}\)

\(=\dfrac{-9}{4}-\dfrac{10}{7}\)

\(=\dfrac{-63}{28}-\dfrac{40}{28}\)

\(=\dfrac{-103}{28}\)

=-9/4-10/7

=-(63/28+40/28)

=-103/28

\(-\dfrac{1}{4}\cdot\dfrac{152}{11}+\dfrac{68}{4}\cdot\dfrac{-1}{4}\)

\(=-\dfrac{1}{4}\left(\dfrac{152}{11}+17\right)\)

\(=-\dfrac{1}{4}\cdot\dfrac{339}{11}=\dfrac{-339}{44}\)

- \(\dfrac{1}{4}\).\(\dfrac{152}{11}\) + \(\dfrac{68}{4}\).\(\dfrac{-1}{4}\)

= - \(\dfrac{1}{4}\).(\(\dfrac{152}{11}\) + \(\dfrac{68}{4}\))

=  - \(\dfrac{1}{4}\). (\(\dfrac{152}{11}\) + \(\dfrac{17}{1}\))

= - \(\dfrac{1}{4}\).(\(\dfrac{152}{11}\) + \(\dfrac{187}{11}\))

= - \(\dfrac{1}{4}\).\(\dfrac{339}{11}\)

 =  - \(\dfrac{339}{44}\)