1) (x+3y)^2 2) (2x-4)^2 3) (3x-1/2)^2 4) (3x-1/2)^2 5) (2x+1)^3 6) (2x-1/2)^3 7) x^2 -4y^2 8) 16x^2-25 9) x^3-27 10) 27x^3y^3 +1
2 câu trả lời
`1) (x+3y)^2`
`=x^2+2.x.3y+(3y)^2`
`=x^2+6xy+9y^2`
`2) (2x-4)^2`
`=(2x)^2-2.2x.4+4^2`
`=4x^2-16x+16`
`3) (3x-1/2)^2`
`=(3x)^2-2.3x.(1)/2+(1/2)^2`
`=9x^2-3x+1/4`
`4) (3x+1/2)^2`
`=(3x)^2+2.3x.(1)/2+(1/2)^2`
`=9x^2+3x+1/4`
`5) (2x+1)^3`
`=(2x)^3+3.(2x)^(2).1+3.2x+1^3`
`=8x^3+12x^2+6x+1`
`6) (2x-1/2)^3`
`=(2x)^3-3.(2x)^2.(1)/2+3.2x.(1/2)^2-(1/2)^3`
`=8x^3-6x^2+3/2x-1/8`
`7) x^2 -4y^2`
`=x^2-(2y)^2`
`=(x-2y)(x+2y)`
`8) 16x^2-25`
`=(4x)^2-5^2`
`=(4x-5)(4x+5)`
`9) x^3-27`
`=x^3-3^3`
`=(x-3)(x^2+3x+9)`
`10) 27x^3y^3 +1`
`=(3xy)^3+1`
`=(3xy+1)(9x^2y^2-3xy+1)`
* Công thức:
1) `(a+b)^2=a^2+2ab+b^2`
2) `(a-b)^2=a^2-2ab+b^2`
3) `a^2-b^2=(a-b)(a+b)`
4) `(a+b)^3= a^3+3a^(2)b+3ab^2+b^3`
5) `(a-b)^3= a^3-3a^(2)b+3ab^2-b^3`
6) `a^3-b^3=(a-b)(a^2+ab+b^2)`
7) `a^3+b^3=(a+b)(a^2-ab+b^2)`
1) (x+3y)² = x² + 2.x.3y + (3y)²
=x² + 6xy + 9y²
2) (2x-4)² = (2x)² - 2.2x.4 + 4²
= 2x² - 16x + 16
3) (3x + $\frac{1}{2}$ )² = (3x)² +2.3x.$\frac{1}{2}$ + ($\frac{1}{2}$)²
= 9x² + 3x + $\frac{1}{4}$
4) (3x - $\frac{1}{2}$ )² = (3x)² - 2.3x.$\frac{1}{2}$ + ($\frac{1}{2}$)²
= 9x² - 3x + $\frac{1}{4}$
5) (2x+1)³ = (2x)³ +3.(2x)².1 + 3.2x.1² +1³
=8x³-12x²-6x+1
6) (2x+$\frac{1}{2}$ )³ = (2x)³ -3.(2x)².$\frac{1}{2}$ + 3.2x.($\frac{1}{2}$)² -($\frac{1}{2}$)³
=8x³-6x²+$\frac{3}{5}$x-$\frac{1}{8}$
7) x²-4y² = x²-(2y)²
=(x-2y).(x+2y)
8) 16x²-25 = (4x)²-5²
= (4x-5).(4x+5)
9) x³-27 = x³-3³
= (x-3).(x²+x.3+3²)
= (x-3).(x²+3x+9)
10) 27x³y³ + 1 = (3xy)³+1³
= (3xy+1).[(3xy)²-3xy.1+1²]
= (3xy+1).(9x²y² - 3xy +1)