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Ta có : -78 x 31 - 78 x 24 - 78 x 17 + 22 x 72
= 78 x (-31 - 24 - 17) + 22 x 72
= -78 x 72 + 22 x 72
= 72 x (-78 + 22)
= 72 x -56
= -4032
Ta có :
\(a\left(a-b\right)-b\left(a-b\right)\)
\(=a^2-ab-ab+b^2\)
\(=a^2-2ab+b^2\)
\(a.\left(a-b\right)-b\left(a-b\right)\)
\(=\left(a-b\right)\left(a-b\right)\)
\(=\left(a-b\right)^2\)
\(\dfrac{2}{3}-4\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\\ =\dfrac{2}{3}-4.\dfrac{2+3}{4}\\ =\dfrac{2}{3}-4.\dfrac{5}{4}\\ =\dfrac{2}{3}-5\\ =\dfrac{2-15}{3}\\ =\dfrac{-13}{3}\)
`a)2/3-4(1/2+3/4)`
`=2/3-4*1/2-4*3/4`
`=2/3-2-3`
`=2/3-5`
`=2/3-15/3`
`=-13/3`
`(3x^3 -2x^2 +3x-2):(x^2+1)`
`=(3x^3 +3x)-(2x^2-2):(x^2+1)`
`=(3x^3 +3x)-(2x^2+2) :(x^2+1)`
`=3x(x^2+1)-2(x^2+1):(x^2+1)`
`=(x^2+1)(3x-2):(x^2+1)`
`=3x-2`
`@ Ariko`
`@` `\text {Ans}`
`\downarrow`
`30 \div { 12*5^2 - 2*[567 - (2*7^2 + 8^2*5)]}`
`= 30 \div {300 - 2*[567 -(98 + 320)]} `
`= 30 \div [300 - 2*(567 - 418)]`
`= 30 \div (300 - 2*149)`
`= 30 \div (300 - 298)`
`= 30 \div 2`
`= 15`
\(30:\left\{12\cdot5^2-2\cdot\left[567-\left(2\cdot7^2+8^2\cdot5\right)\right]\right\}\)
\(=30:\left\{12\cdot5^2-2\cdot\left[567-\left(98+320\right)\right]\right\}\)
\(=30:\left[300-2\cdot\left(567-418\right)\right]\)
\(=30:\left(300-2\cdot158\right)\)
\(=30:\left(300-316\right)\)
\(=30:-16\)
\(=-\dfrac{15}{8}\)
\(3^2\cdot5^2-\left\{4^3\cdot25-3\cdot\left[3\cdot\left(17+3\right)^3-7\cdot10^2\right]\right\}\)
\(=\left(3\cdot5\right)^2-\left[64\cdot25-3\cdot\left(3\cdot20^3-7\cdot100\right)\right]\)
\(=15^2-\left[8^2\cdot5^2-3\cdot\left(3\cdot8000-700\right)\right]\)
\(=225-\left[\left(5\cdot8\right)^2-3\cdot\left(24000-700\right)\right]\)
\(=225-\left(40^2-3\cdot23300\right)\)
\(=225-\left(1600-69900\right)\)
\(=225-\left(-68300\right)\)
\(=68525\)
\(\left[\left(\dfrac{5}{2}\right)^2-2\left(\dfrac{-1}{3}\right)^2+2\right]-\left(\dfrac{-1}{3}\right)^3=\left[\dfrac{25}{4}-\dfrac{2}{9}+2\right]+\dfrac{1}{27}=\dfrac{289}{36}+\dfrac{1}{27}=\dfrac{871}{108}\)
`@` `\text {Ans}`
`\downarrow`
`c)`
`[ (5/2)^2 - 2*(-1/3)^2 + 2] - (-1/3)^3`
`= (25/4 - 2*1/9 + 2) - (-1/27)`
`= (25/4 - 2/9 + 2) + 1/27`
`= 217/36 + 2 + 1/27`
`= 289/36 + 1/27`
`= 871/108`
\(\left(\dfrac{-1}{3}\right)^2-\left[\left(-\dfrac{5}{2}\right)-\left(1,5-\dfrac{8}{3}\right)\right]=\dfrac{1}{9}-\left[\left(\dfrac{-5}{2}\right)-\left(\dfrac{-7}{6}\right)\right]=\dfrac{1}{9}-\left(\dfrac{-4}{3}\right)=\dfrac{13}{9}\)
(-1/3)² - [(-5/2) - (1,5 - 8/3)]
= 1/9 - (-5/2 + 7/6)
= 1/9 + 4/3
= 13/9
\(A=\dfrac{16^4.81^3}{9^5.9^4}\)
\(=\dfrac{\left(2^4\right)^4.\left(3^4\right)^3}{9^9}\)
\(=\dfrac{2^{16}.3^{12}}{\left(3^2\right)^9}\)
\(=\dfrac{2^{16}.3^{12}}{3^{18}}\)
\(=\dfrac{2^{16}}{3^6}\)