Phân tích đa thức thành nhân tử à?

1) \(\left(x+y\right)^3-x^3-y^3\)

\(=\left(x+y\right)^3-\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(=\left(x+y\right)\left[\left(x+y\right)^2-x^2+xy-y^2\right]\)

\(=\left(x+y\right)\left(x^2+2xy+y^2-x^2+xy-y^2\right)\)

\(=3xy\left(x+y\right)\)

2) \(x^3+1-x^2-x\)

\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)

\(=\left(x+1\right)\left[x^2-x+1-x\right]\)

\(=\left(x+1\right)\left(x^2-2x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)^2\)

( x + y )³ - x³ - y³

= ( x + y )³ - ( x³ + y³ )

= ( x + y )³ - ( x + y )( x² - xy + y² )

= ( x + y )[ ( x + y )² - ( x² - xy + y² ) ]

= ( x + y )( x² + 2xy + y² - x² + xy - y² )

= 3xy( x + y )

x³ + 1 - x² - x

= ( x³ + 1 ) - ( x² + x )

= ( x + 1 )( x² - x + 1 ) - x( x + 1 )

= ( x + 1 )( x² - x + 1 - x )

= ( x + 1 )( x² - 2x + 1 )

= ( x + 1 )( x - 1 )²

7^2 x 3 - 5^2 x 3

= 3 x ( 7^2 - 5^2 )

= 3 x ( 49 - 25 )

= 3 x 24

= 72 

7\(^2\)x3-5\(^2\)x3

=49x(-22)x3

=-3234

a)\(3^8:3^4+2^2.2^3\)\(=3^4+2^5\)

                                    \(=81+32\)

                                    \(=113\)

b)\(3.4^2-2.3=3.\left(4^2-3\right)\)

                          \(=3.13\)

                          \(=39\)

Học tốt nha!!!

10³ + 2¹⁵

= 1000 + 32768

= 33768

Mà 33768 : 33 = 1023 (dư 9)

Em xem lại đề

\(2^{x+1}-2^x=3^2\)

\(\Rightarrow2^x\cdot\left(2-1\right)=9\)

\(\Rightarrow2^x=9\)

\(\Rightarrow x\in\varnothing\)

\(2^{x+1}-2^x=3^2\)

=>2^x*2-2^x=9

=>2^x=9

=>\(x\in\varnothing\)

`@` `\text {Ans}`

`\downarrow`

`(2^2+1) \times (x+14) = 5^2 \times 4 + (2^5 + 3^2 + 7^2) \div 2`

` \Rightarrow (4+1) \times (x+14) = 5^2\times 2^2 + ( 32 + 9 + 49) \div 2`

`\Rightarrow 5 \times (x+14) = (5*2)^2 + (32+58) \div 2`

`\Rightarrow 5 \times (x+14) = 10^2+90 \div 2`

`\Rightarrow 5 \times (x+14) = 100 + 45`

`\Rightarrow 5 \times (x+14) = 145`

`\Rightarrow x+14 = 145 \div 5`

`\Rightarrow x+14=29`

`\Rightarrow x=29-14`

`\Rightarrow x=15`

Vậy, `x=15.`

\(\left(2^2+1\right)\cdot\left(x+14\right)=5^2\cdot4+\left(2^5+3^2+7^2\right):2\)

\(\Rightarrow\left(4+1\right)\cdot\left(x+14\right)=25\cdot4+\left(32+9+49\right):2\)

\(\Rightarrow5\cdot\left(x+14\right)=100+45\)

\(\Rightarrow5x+70=145\)

\(\Rightarrow5x=75\)

\(\Rightarrow x=\dfrac{75}{5}=15\)

a: \(=25x^4-10x^3+5x^2\)

c: \(=2x^3-3x-5x^3-x^2+x^2=-3x^3-3x\)

\(\Rightarrow2S=6+\frac{3}{1}+\frac{3}{2}+...+\frac{3}{2^8}\)

\(\Rightarrow2S-S=\left(6+3+\frac{3}{2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+...+\frac{3}{2^9}\right)\)

\(\Rightarrow S=3-\frac{3}{2^9}\)

\(S=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^9}\)

\(\Rightarrow\frac{1}{2}.S=\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{10}}\)

\(\Rightarrow S-\frac{1}{2}.S=\frac{1}{2}.S=3+\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^9}-\left(\frac{3}{2}+\frac{3}{2^2}+\frac{3}{2^3}+...+\frac{3}{2^{10}}\right)\)

\(\Rightarrow\frac{1}{2}.S=3-\frac{3}{2^{10}}\)

\(\Rightarrow S=6-\frac{6}{2^{10}}\)