Bài 5: Những hằng đẳng thức đáng nhớ (Tiếp)

`4)27x^3-125=(3x-5)(9x^2+15x+25)`

`5)(2y-5)(4y^2+10y+25)=(2y)^3-5^3=8y^3-125`

`6)(3y-4)(9y^2+12y+16)=(3y)^3-4^3=27y^3-64`

`7)(x-3)^3+(2-x)^3=(x-3+2-x)[(x-3)^2-(x-3)(2-x)+(2-x)^2]=-(x^2-6x+9-2x+x^2+6-3x+4-4x+x)=-2x^2+14x-19`

`8)(x+y)^3-(x-y)^3=(x+y-x+y)[(x+y)^2+(x-y)(x+y)+(x-y)^2]=2y(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)=6x^2y+2y^3`

a: \(=\left(x+4\right)\left(x^2-4x+16\right)\)

b: \(=x^3-6x^2+12x-8+x^3+3x^2+3x+1\)

\(=2x^3-3x^2+15x-7\)

c: \(=27x^3+64\)

(3a + 2)² + 2(2 + 3a) (1 - 2b) + (2b - 1)²

= (3a)² + 2.3a.2 + 2² + 2(2 + 3a) (1 - 2b) + (2b)² + 2.2b.1 + 1²

= 9a² + 12a + 4 + (2(2 + 3a) (1 - 2b) + 4b² + 4b + 1

\(\Leftrightarrow4x^2-12x+9+4x^2+12x+9=4x^2+3x\)

=>8x^2+18=4x^2+3x

=>4x^2-3x+18=0

hay \(x\in\varnothing\)

\(a, 3x\left(x-1\right)^2-2x\left(x+3\right)\left(x-3\right)+4x\left(x-4\right)\)
\(=3x\left(x^2-2x+1\right)-2x\left(x^2-9\right)+4x^2-16x\)
\(=3x^3-6x^2+3x-2x^3+18x+4x^2-16x\)
\(=x^3-2x^2+5x\)
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\(b,\left(x+2\right)\left(x^2-2x+4\right)+\left(x-3\right)\left(x^2+3x+9\right)+19\)
\(=x^3+8+x^3-27+19\)
\(=2x^3\)

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

\(=3x^3-6x^2+3x-2x^3+18x+4x^2-16x\)

\(=x^3-2x^2+5x\)

b: \(=x^3+8+x^3-27+19=2x^3\)

a: \(=x^2+3x+\dfrac{9}{4}-\dfrac{13}{4}=\left(x+\dfrac{3}{2}\right)^2-\dfrac{13}{4}>=-\dfrac{13}{4}\)

Dấu = xảy ra khi x=-3/2

b: \(=2\left(x^2-\dfrac{5}{2}x-2\right)\)

\(=2\left(x^2-2\cdot x\cdot\dfrac{5}{4}+\dfrac{25}{16}-\dfrac{57}{16}\right)\)

\(=2\left(x-\dfrac{5}{4}\right)^2-\dfrac{57}{8}>=-\dfrac{57}{8}\)

Dấu '=' xảy ra khi x=5/4

`a)x^2-x-6=x^2-3x+2x-6=(x-3)(x+2)`

`b)x^4+4x^2-5=x^4+5x^2-x^2-5=(x^2+5)(x^2-1)=(x^2+5)(x-1)(x+1)`

`c)x^3-19x-30=x^3-5x^2+5x^2-25x+6x-30=(x-5)(x^2+5x+6)=(x-5)(x^2+3x+2x+6)=(x-5)(x+2)(x+3)`

đừng ghi kết quả luôn nha!

\(a,\left(3x+4\right)^2-\left(3x-1\right)\left(3x+1\right)=49\\ =>9x^2+24x+16-9x^2+1=49\\ =>24x+17=49\\ =>24x=32\\ =>x=\dfrac{4}{3}\\ b,x^2-81=0\\ =>\left[{}\begin{matrix}x-9=0\\x+9=0\end{matrix}\right.=>\left[{}\begin{matrix}x=9\\x=-9\end{matrix}\right.\)

\(a,10y^2+2y=2y\left(5y+1\right)\\ b,3z^2+6zy+3y^2-27\times2=3\left(z^2+2zy+y^2\right)-54\\ =3.\left(z+y\right)^2-54\)