\(a,\left(a^3-b^3\right)+\left(a-b\right)^2\)

\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)

\(=\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)

\(b,\left(x^2+1\right)^2-4x^2\)

\(=x^4+2x^2+1-4x^2\)

\(=x^4-2x^2+1\)

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

\(c\left(y^3+8\right)+\left(y^2-4\right)\)

\(=\left(y+2\right)\left(y^2-8y+4\right)+\left(y-2\right)\left(y+2\right)\)

\(=\left(y+2\right)\left(y^2-8y+4+y-2\right)\)

\(=\left(y+2\right)\left(y^2-7y+2\right)\)

a) ( a³ - b³) + ( a - b)²

= (a-b) (a² + ab + b² ) + (a-b)²

= (a-b) (a² + ab + b² +a -b ) 

hok tốt

\(\left(4x-1\right)^2+\left(x+3\right)^2=16x^2-8x+1+x^2+6x+9\)

\(=17x^2-2x+10\)

\(\left(x-y+1\right)^3=x^3-y^3+1-3x^2y+3xy^2+3x^2+3x+3y^2-3y-6xy\)

\(\left(4x-1\right)^2+\left(x+3\right)^2=16x^2-8x+1+x^2+6x+9\) \(=17x^2-2x+10\)

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

-x³ + x² + 4 = 0

<=> -(x - 2)(x² + x + 2) = 0

<=> x - 2 = 0

       x = 0 + 2

       x = 2

Mà vì x² + x + 2 # 0 

=> x = 2

\(\left(-\frac{7}{4}\right)^2+\left(-\frac{3}{4}\right)^9.64-2018^0=\frac{49}{16}+\left(-\frac{19683}{262144}\right).64-1\)

\(=\frac{49}{16}-\frac{19683}{4096}-1\)\(=\frac{12544-19683-4096}{4096}\)

\(=-\frac{11235}{4096}\)

\(P=y^2+8y+15\)

\(=\left(y^2+8y+16\right)-1\)

\(=\left(y+4\right)^2-1\ge-1\)

Dấu "=" xảy ra khi \(y=-4\)

\(2x^2+5y^2+4xy+8x-4y-100\)

\(=\left(x^2+4xy+4y^2\right)+\left(x^2+8x+16\right)+\left(y^2-4y+4\right)-120\)

\(=\left(x+2y\right)^2+\left(x+4\right)^2+\left(y-2\right)^2-120\)

\(\ge-120\)

Dấu "=" xảy ra khi \(\hept{\begin{cases}x+2y=0\\x+4=0\\y-2=0\end{cases}}\Rightarrow y=2;x=-4\)

1995 + 1997 = 3992

1995 + 1997 = 3992