a) \(x^3-x\)
\(=x\left(x^2-1\right)\)
\(=x\left(x+1\right)\left(x-1\right)\)
b) \(\left(2x+y\right)^2-4y^2\)
\(=\left(2x+y-2y\right)\left(2x+y+2y\right)\)
\(=\left(2x-y\right)\left(2x+3y\right)\)
c) \(x^3+y^3+x+y\)
\(=\left(x^3+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+xy+y^2\right)+\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+xy+y^2+1\right)\)
d) \(x^3+4x^2y+4xy^2-9x\)
\(=x\left(x^2+4xy+4y^2-9\right)\)
\(=x\left[\left(x+2y\right)^2-3^2\right]\)
\(=x\left(x+2y-3\right)\left(x+2y+3\right)\)
e) \(x^2+4-y^2+4x\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
f) \(x^4+4\)
\(=x^4+2x^3+2x^2-2x^3-4x^2-4x+2x^2+4x+4\)
\(=\left(x^4+2x^3+2x^2\right)-\left(2x^3+4x^2+4x\right)+\left(2x^2+4x+4\right)\)
\(=x^2\left(x^2+2x+2\right)-2x\left(x^2+2x+2\right)+2\left(x^2+2x+2\right)\)
\(=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)
1) Tìm x a. (4x - 1 )² - 8 ( x - 2 ) ( 3 + 2x ) = 15 b. ( 5x - 2 ) ( x - 2 ) - 4 ( x - 3 ) = x² + 3 2) pt đa thức thành nhân tử a. 5x² - 10xy + 5y² - 20z² b. a³ - ay - a²x + xy c. 3x² - 6xy + 3y² - 12z² d. x² - y² + 2yz - z² e. x² - 2xy + tx - 2ty mình cảm ơn ạ
1)
a) => 16x2 - 8x + 1 - 8(2x2 + 3x - 4x - 6) = 15
=> 16x2 - 8x + 1 - 8(2x2 - x - 6) = 15
=> 16x2 - 8x + 1 - 16x2 + 8x + 48 = 15
=> 49 = 15 (?) (vô lí)
=> Không tìm được x thoả mãn
b) (5x - 2)(x - 2) - 4(x - 3) = x2 + 3
=> 5x2 - 10x - 2x + 4 - 4x + 12 = x2 + 3
=> 5x2 - 16x + 16 = x2 + 3
=> 4x2 - 16x + 16 = 3
=> (2x)2 - 2.2x.4 + 42 = 3
=> (2x - 4)2 = 3
=> \(\left[{}\begin{matrix}2x-4=\sqrt{3}\\2x-4=-\sqrt{3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4+\sqrt{3}}{2}\\x=\dfrac{4-\sqrt{3}}{2}\end{matrix}\right.\)
Mong bạn xem lại đề bài!
2)
a) 5x2 - 10xy + 5y2 - 20z2
= 5(x2 - 2xy + y2 - 4z2)
= 5[(x - y)2 - (2z)2]
= 5(x - y - 2z)(x - y + 2z)
b) a3 - ay - a2x + xy
= a(a2 - y) - x(a2 - y)
= (a - x)(a2 - y)
c) 3x2 - 6xy + 3y2 - 12z2
= 3(x2 - 2xy + y2 - 4z2)
= 3[(x - y)2 - (2z)2]
= 3(x - y - 2z)(x - y + 2z)
d) x2 - 2xy + tx - 2ty
= x(x - 2y) + t(x - 2y)
= (x + t)(x - 2y)
phân tích đa thức thành nhân tử
(3x+1)^2-(3x-1)^2
(x+y)^2-(x-y)^2
(x+y)^3-(x-y)^3
x^3+y^3+z^3-3xyz
\(\left(3x+1\right)^2-\left(3x-1\right)^2\)
\(=\left(3x+1-3x+1\right)\left(3x+1+3x-1\right)\)
\(=2\cdot6x\)
\(=12x\)
_________
\(\left(x+y\right)^2-\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)\left(x+y-x+y\right)\)
\(=2x\cdot2y\)
\(=4xy\)
\(\left(x+y\right)^3+\left(x-y\right)^3\)
\(=\left(x+y+x-y\right)\left[\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=2x\cdot\left(x^2+2xy+y^2-x^2+y^2+x^2-2xy+y^2\right)\)
\(=2x\cdot\left(x^2+3y^2\right)\)
______
\(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3-3xy\left(x-y\right)+z^3+3xyz\)
\(=\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)^3-3z\left(x+y\right)\left(x+y+z\right)-3xy\left(x-y-z\right)\)
\(=\left(x+y+z\right)\left[\left(x+y+z\right)^2-3z\left(x+y\right)-3xy\right]\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2+2xy+2xz+2yz-3xz-3yz-3xy\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2-xy-xz-yz\right)\)
tìm x biết
x-3=(3-x)^2
x^3+3/2x^2+3/4x+1/8=1/64
\(\left(x-3\right)=\left(3-x\right)^2\)
\(\Leftrightarrow x-3=\left(x-3\right)^2\)
\(\Leftrightarrow\left(x-3\right)-\left(x-3\right)^2=0\)
\(\Leftrightarrow\left(x-3\right)\left[1-\left(x-3\right)\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(4-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\4-x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
___________
\(x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}=\dfrac{1}{64}\)
\(\Leftrightarrow x^3+3\cdot\dfrac{1}{2}\cdot x^2+3\cdot\left(\dfrac{1}{2}\right)^2\cdot x+\left(\dfrac{1}{2}\right)^3=\dfrac{1}{64}\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^3=\left(\dfrac{1}{4}\right)^3\)
\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{1}{4}\)
\(\Leftrightarrow x=\dfrac{1}{4}-\dfrac{1}{2}\)
\(\Leftrightarrow x=-\dfrac{1}{4}\)
Tính nhanh giáo trị biểu thức 72^2+144*16+16^2-12^2
\(72^2+144\cdot16+16^2-12^2\)
\(=\left(72^2+144\cdot16+16^2\right)-12^2\)
\(=\left(72^2+2\cdot72\cdot16+16^2\right)-12^2\)
\(=\left(72+16\right)^2-12^2\)
\(=88^2-12^2\)
\(=\left(88+12\right)\left(88-12\right)\)
\(=100\cdot76\)
\(=7600\)
Tính nhanh giáo trị biểu thức 48^2-42^2+64-52^2
\(48^2-42^2+64-52^2\)
\(=\left(48^2-52^2\right)-\left(42^2-64\right)\)
\(=\left(48^2-52^2\right)-\left(42^2-8^2\right)\)
\(=\left(48-52\right)\left(48+52\right)-\left(42+8\right)\left(42-8\right)\)
\(=-4\cdot100-50\cdot34\)
\(=-8\cdot50-50\cdot34\)
\(=-50\cdot\left(8+34\right)\)
\(=-50\cdot42\)
\(=-2100\)
a: =(x+2)^3
b: =(x-1)^3
c: =(1-3x)^3
d: =(x+1/2)^3
e: =(3x-2y)^3
a: =(x-5)^2(x+5)^2-(x-5)^2
=(x-5)^2[(x+5)^2-1]
=(x-5)^2*(x+5-1)(x+5+1)
=(x+4)(x+6)(x-5)^2
b: =(2x-5)^2*(2x+5)^2-9(2x-5)^2
=(2x-5)^2[(2x+5)^2-9]
=(2x-5)^2(2x+5-3)(2x+5+3)
=4(x+4)(x+1)(2x-5)^2
c: =(2x-3)^2[4-9(2x+3)^2]
=(2x-3)^2*[2^2-(6x+9)^2]
=(2x-3)(2-6x-9)(2+6x+9)*(2x-3)
=(-6x-7)(11+6x)(2x-3)^2
d: =a^2(a^4-a^2+2a+2)
=a^2[a^2(a-1)(a+1)+2(a+1)]
=a^2(a+1)(a^2-a+2)
e: =(3x^2+3x+2-3x^2-3x+2)(3x^2+3x+2+3x^2+3x-2)
=(6x^2+6x)*4
=24x(x+1)
phân tích thành nhân tử
a(b^2 +c^2) +b( c^2 + a^2) +c(a^2+b^2) + abc
(a+b)(a^2-b^2)+ (b+c)(b^2- c^2)+(c+a)(c^2-a^2)
phân ích thành nhân tử
ab(a+b) -bc(b+c) +ac(a-c)
ab(a+b) - bc(b + c) + ac(a - c)
=a2b + ab2 - b2c - bc2 + a2c - ac2
=(ab2 - b2c) + (a2c - ac2) + (a2b - bc2)
=b2(a - c) + ac(a - c) + b(a2 - c2)
=b2(a - c) + ac(a - c) + b(a - c)(a + c)
=(a - c )[b2 + ac + b(a + c)]
=(a - c)[(b2 + bc) + (ab + ac)]
=(a - c)[b(b + c) + a(b + c)]
=(a - c)(a + b)(b + c)