a) \(a^4+b^4\)

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

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

b) Tương tự 

c) \(a^5+b^5\)

\(=\left(\sqrt{a}^5\right)^2+\left(\sqrt{b}^5\right)^2\)

\(=\left(\sqrt{a}^5+\sqrt{b}^5\right).\left(\sqrt{a}^5-\sqrt{b}^5\right)\)

\(=2\left(m^2-10m+7\right)=2\left(m^2-10m+25-18\right)\)

\(=2\left(m^2-10m+25\right)-36=2\left(m-5\right)^2-36\ge-36\)  \(\forall m\)

Ta có:  x⁶ -y⁶= (x³)²  -(y³)²  = (x³  - y³)(x³ + y³)

\(x^6-y^6\)

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

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

hk 

tốt

\(a,x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right).\)

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

\(b,9x^2+y^2+6xy=\left(3x\right)^2+2.3x.y+y^2=\left(3x+y\right)^2\)

\(c,6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x^2-2.x.3+3^2\right)=-\left(x-3\right)^2\)

2) 9x²+ 12x+ 4

<=>(3x)²+ 2.3x.2+ 2² <=>(3x+ 2)²

3) 4x⁴+ 20x²+ 25

<=>(2x²)²+ 2.2x².5+ 5² <=>(2x²+5)²

4) 25x²- 20xy+ 4y²

<=> (5x)²- 2.5x.2y+ (2y)²<=> (5x-2y)²

5) 9x⁴- 12x²y+ 4y²

<=> (3x²)²- 2.3x².2.y+ (2y)²<=> (3x²- 2y)²

6) 4x⁴- 16x²y³+ 16y⁶

<=> (2x²)²- 2.2x².4y³+ (4y³)²<=> (2x²- 4y³)²

7) 9x⁴- 12x⁵+ 4x⁶

<=> (3x²)²- 2.3x².2x³+ (2x³)²<=> (3x²- 2x³)²

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

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

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

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

5: \(\left(x+2\right)^3=x^3+6x^2+12x+8\)

a) = a³+b³+c³ +3a²b +3ab² -3ab(a+b) - 3abc

= (a+b)³+c³-3ab(a+b)-3abc (áp dụng A³+B³ ta có)

=(a+b+c) ( (a+b)² - (a+b)c +c²) - 3ab(a+b+c)

=(a+b+c) ( (a+b)² - (a+b)c +c² - 3ab) (nhân tử chung là a+b+c)

=(a+b+c) ( a²+2ab+b²- ac-bc +c² -3ab)

=(a+b+c) (a²+b²+c²-ab-ac-bc)

Phần b tương tự