\(\frac{x^5y}{\left(xy\right)^4}\)

\(=\frac{x^5y}{x^4y^4}=\frac{x}{y^3}\)

\(x^2-x-30\)

\(=x^2+5x-6x-30\)

\(=x\left(x+5\right)-6\left(x+5\right)\)

\(=\left(x+5\right)\left(x-6\right)\)

\(x^2+5x-6x-30\)

\(=x\left(x+5\right)-6\left(x+5\right)\)

\(=\left(x-6\right)\left(x+5\right)\)

Tính a, x²+y²

=  x² + 2xy + y² - 2xy

= ( x + y )² - 2xy

Thay x + y = 3 và x.y = 2

=> 3² - 2 . 2

= 9 - 4

= 5

Mấy cái sau cũng tách ra nhá 

(5n - 2)² - (2n - 5)²

= 25n² - 20n + 4 - 4n² + 20n - 25

= 21n² - 21

= 21(n² - 1) \(⋮\) 21 (đpcm)

Mình nhanh nhất, chọn mình nha

\(\frac{x^5y}{xy^4}=\frac{x^4}{y^3}\)

\(\frac{3\times x^2\times y^5}{9\times x\times y^4}=\frac{xy}{3}\)

a)=(x+1/4)^2=100^2=10000

b) =x^2-(y+1)^2=(x-y-1)(x+y+1)=86.100=8600

bằng 20

\(\text{a) }4x^{16}+81=4x^4+36x^2+81-36x^8\)

                          \(=\left(4x^{16}+36x^8+81\right)-36x^8\)

                          \(=\left[\left(2x^8\right)^2+2.2x^8.9+9^2\right]+\left(6x^4\right)^2\)

                          \(=\left(2x^8+9\right)^2-\left(6x^4\right)^2\)

                         \(=\left(2x^8+9-6x^4\right)\left(2x^8+9+6x^4\right)\)                    

\(\text{b) }x^4+2018x^2+2017x+2018\)

\(=x^4+2018x^2+2018x-x+2018\)

\(=\left(x^4-x\right)+\left(2018x^2+2018x+2018\right)\)

\(=x\left(x^3-1\right)-2018\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2018\left(x^2+x+1\right)\)

\(=\left(x^2-x\right)\left(x^2+x+1\right)+2018\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2018\right)\)

Với a, b  thuộc Z và không chia hết cho 7

Theo định lí fecmat:  \(a^6\equiv1\left(mod7\right)\); \(b^6\equiv1\left(mod7\right)\)(1)

Đặt: \(a^6=u;b^6=v\)

Ta có: \(a^{42}-b^{42}=u^7-v^7=\left(u-v\right)\left(u^6+u^5v+u^4v^2+u^3v^3+u^2v^4+uv^5+v^6\right)\)

Từ (1) => \(u-v\equiv1-1\equiv0\left(mod7\right)\)=> \(u-v⋮7\)

và  \(u^6;u^5v;u^4v^2;u^3v^3;u^2v^4;uv^5;v^6\equiv1\left(mod7\right)\) 

\(\Rightarrow u^6+u^5v+u^4v^2+u^3v^3+u^2v^4+uv^5+v^6\equiv1+1+1+1+1+1+1\equiv7\equiv0\left(mod7\right)\)

=> \(u^6+u^5v+u^4v^2+u^3v^3+u^2v^4+uv^5+v^6⋮7\)

=> \(\left(u-v\right)\left(u^6+u^5v+u^4v^2+u^3v^3+u^2v^4+uv^5+v^6\right)⋮49\)