17) 8x3 + 27
18) a6 - 1
19) 2x3 - 1
20) 9x4 - 81x2
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H9
HT.Phong (9A5)
CTVHS
28 tháng 10 2023
\(\dfrac{7}{2}\times\dfrac{3}{4}+\dfrac{17}{8}\times\dfrac{2}{3}+\dfrac{3}{4}\times\dfrac{1}{2}+\dfrac{7}{8}\times\dfrac{3}{3}\)
\(=\dfrac{7\times3}{2\times4}+\dfrac{17\times2}{8\times3}+\dfrac{3\times1}{4\times2}+\dfrac{7}{8}\times1\)
\(=\dfrac{21}{8}+\dfrac{17}{12}+\dfrac{3}{8}+\dfrac{7}{8}\)
\(=\left(\dfrac{21}{8}+\dfrac{3}{8}+\dfrac{7}{8}\right)+\dfrac{17}{12}\)
\(=\dfrac{31}{8}+\dfrac{17}{12}\)
\(=\dfrac{31\times3}{8\times3}+\dfrac{17\times2}{12\times2}\)
\(=\dfrac{93}{24}+\dfrac{34}{24}\)
\(=\dfrac{127}{24}\)
17 tháng 8 2021
a: \(50x^5-8x^3\)
\(=2x^3\left(25x^2-4\right)\)
\(=2x^3\left(5x-2\right)\left(5x+2\right)\)
b: \(x^4-5x^2-4y^2+10y\)
\(=\left(x^2-2y\right)\left(x^2+2y\right)-5\left(x^2-2y\right)\)
\(=\left(x^2-2y\right)\left(x^2+2y-5\right)\)
c: \(36a^2+12a+1-b^2\)
\(=\left(6a+1\right)^2-b^2\)
\(=\left(6a+1-b\right)\left(6a+1+b\right)\)
d: \(x^3+y^3-xy^2-x^2y\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-xy\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-2xy+y^2\right)\)
\(=\left(x+y\right)\cdot\left(x-y\right)^2\)
17 tháng 8 2021
e: Ta có: \(4x^2+4x-3\)
\(=4x^2+6x-2x-3\)
\(=2x\left(2x+3\right)-\left(2x+3\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
f: Ta có: \(9x^4+16x^2-4\)
\(=9x^4+18x^2-2x^2-4\)
\(=9x^2\left(x^2+2\right)-2\left(x^2+2\right)\)
\(=\left(x^2+2\right)\left(9x^2-2\right)\)
g: Ta có: \(-6x^2+5xy+4y^2\)
\(=-6x^2+8xy-3xy+4y^2\)
\(=-2x\left(3x-4y\right)-y\left(3x-4y\right)\)
\(=\left(3x-4y\right)\left(-2x-y\right)\)
h: Ta có: \(\left(x^2+4x\right)^2+8\left(x^2+4x\right)+15\)
\(=\left(x^2+4x\right)^2+3\left(x^2+4x\right)+5\left(x^2+4x\right)+15\)
\(=\left(x^2+4x+3\right)\cdot\left(x^2+4x+5\right)\)
\(=\left(x+1\right)\left(x+3\right)\left(x^2+4x+5\right)\)
2 tháng 10 2021
Bài 1:
a: \(8x^3-2x=2x\left(4x^2-1\right)=2x\left(2x-1\right)\left(2x+1\right)\)
c: \(-5m^3\left(m+1\right)+m+1=\left(m+1\right)\left(-5m^3+1\right)\)
3 tháng 10 2021
a: Ta có: \(2\left(x-2\right)^3=2-x\)
\(\Leftrightarrow2\left(x-2\right)^3+x-2=0\)
\(\Leftrightarrow x-2=0\)
hay x=2
b: ta có: \(8x^3-72x=0\)
\(\Leftrightarrow x\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\)
c: Ta có: \(2x^3+3x^2+2x+3=0\)
\(\Leftrightarrow2x+3=0\)
hay \(x=-\dfrac{3}{2}\)
21 tháng 8 2021
1, \(a^6+b^3=\left(a^2+b\right)\left(a^4-a^2b+b^2\right)\)
2, \(x^2-10x+25=\left(x-5\right)^2\)
3, \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
4, \(x^2+4xy+4y^2=\left(x+2y\right)^2\)
21 tháng 8 2021
1) \(a^6+b^3=\left(a^2\right)^3+b^3=\left(a^2+b\right)\left(a^4-a^2b+b^2\right)\)
2) \(x^2-10x+25=\left(x-5\right)^2\)
3) \(8x^3-\dfrac{1}{8}=\left(2x\right)^3-\left(\dfrac{1}{3}\right)^3=\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2x}{3}+\dfrac{1}{4}\right)\)
4) \(x^2+4xy+4y^2=\left(x+2y\right)^2\)
18 tháng 10 2021
a: Ta có: \(-\left(-3x^2\right)^3+4x-9-27x^6\)
\(=27x^6-27x^6+4x-9\)
=4x-9
=-1
HK
1
20 tháng 3 2023
a: \(=\dfrac{1}{2}\cdot\dfrac{3}{4}\cdot\dfrac{5}{6}=\dfrac{15}{48}=\dfrac{5}{16}\)
b: \(=\dfrac{2}{3}+\dfrac{12}{42}=\dfrac{2}{3}+\dfrac{2}{7}=\dfrac{20}{21}\)
c: \(=\dfrac{24}{5}\cdot\dfrac{5}{12}=2\)
d: \(=\dfrac{1}{9}+\dfrac{3}{4}=\dfrac{4+27}{36}=\dfrac{31}{36}\)
17) \(8x^3+27=\left(2x\right)^3+3^3=\left(2x+3\right)\left(4x^2-6x+9\right)\)
18) \(a^6-1=\left(a^3\right)^2-1=\left(a^3-1\right)\left(a^3+1\right)=\left(a-1\right)\left(a^2+a+1\right)\left(a+1\right)\left(a^2-a+1\right)\)
20) \(9x^4-81x^2=9\left(x^4-9x^2\right)=9x^2\left(x^2-9\right)=9x^2\left(x-3\right)\left(x+3\right)\)
17)
\(8x^3+27=\left(8x\right)^3+3^3=\left(8x+3\right)\left(64x^2-24x+9\right)\)
18)
\(a^6-1=\left(a^3\right)^2-1\)
\(=\left(a^3-1\right)\left(a^3+1\right)\)
\(=\left(a-1\right)\left(a^2-a+1\right)\left(a+1\right)\left(a^2+a+1\right)\)
19)
đề sao sao ý
20)
\(=\left(3x^2\right)^2-\left(9x\right)^2\)
\(=\left(3x^2-9x\right)\left(3x^2+9x\right)\)
\(=3x\left(x-9\right)3x\left(x+9\right)=9x^2\left(x-9\right)\left(x+9\right)\)