a) Ta có : \(\left(x+y\right)^3=1^3=1\)

\(\Leftrightarrow x^3+y^3+3xy\left(x+y\right)=1\)

\(\Leftrightarrow x^3+y^3+3xy=1\) ( do x + y = 1 )

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

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

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

Vs x = 1/2 ; y = 3 ⇒ \(A=\frac{1}{4}.4=1\)

\(B=3x^2-6xy+y^2-2x^2-4xy-2y^2-x^2+y^2=-10xy=\frac{1}{2}.3.10=15\)

\(C=x^3+3x^2y+3xy^2+y^2-x^3+3x^2y-3xy^2+y^3-6x^2y-1=2y^2-1=18-1=17\)\(D=x^3+y^3-x^3-3x^2y-3xy^2-y^3=-3x^2y-3xy^2=\frac{1}{4}.9+\frac{1}{2}.27=\frac{9}{4}+\frac{108}{4}=\frac{117}{4}\)Check lại nhé <33 sợ sai lém

a: \(F=x^3y^2z-xy^2z^3\)

Khi x=3; y=-2; z=1 thì \(F=3^3\cdot\left(-2\right)^2\cdot1-3\cdot\left(-2\right)^2\cdot1^3=27\cdot4-3\cdot4=96\)

c: x=-y; y=2z

nên x=-2z

Thay x=-2z; y=2z vào F=-1/8, ta được:

\(\left(-2z\right)^3\cdot\left(2z\right)^2\cdot z-\left(-2z\right)\cdot\left(2z\right)^2\cdot z^3=\dfrac{-1}{8}\)

=>\(-8z^3\cdot4z^2\cdot z+2z\cdot4z^2\cdot z^3=\dfrac{-1}{8}\)

\(\Leftrightarrow-24z^6=\dfrac{-1}{8}\)

\(\Leftrightarrow z^6=\dfrac{1}{192}\)

hay \(z=\pm\dfrac{1}{2\sqrt{3}}\)

help me

1.Tính:

[(x+y)⁵-2(x+y)⁴ ] : [-5(x+y)³]

= -5(x+y)² + \(\dfrac{2}{5}\)(x+y)

2.Tìm a để đa thức 24x³ -14x² +23x+2a+4 \(⋮\) 4x+1

24x³ -14x² +23x+2a+4 \(|^{4x+1}_{6x^2-5x+7}\)

24x³ +6x²

\(\overline{-20x^2}+23x+2a+4\)

-20x² -5x

\(\overline{28x+2a+4}\)

28x +7

\(\overline{2a+11}\)

Để 24x³ -14x² +23x+2a+4 \(⋮\) 4x+1 thì 2a+11=0 \(\Leftrightarrow\) a= \(\dfrac{11}{2}\)

3. Phân tích đa thức thành NT :

a, 12x³ -12x² +3x = 3x(4x² -4x+1) = 3x (2x+1)

b, x².(x-1)+9(1-x) = x² (x-1) -9(x-1) = (x-1)(x²-9)

=(x-1)(x-3)(x+3)

c,8(x-y)-x³ (x-y) = (x-y)(8-x³)= (x-y)(2-x)(4+2x+x²)

Bài 4: 

=>x^2-x+1/4=0

=>(x-1/2)^2=0

=>x-1/2=0

=>x=1/2

Bài 5: 

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

=>\(2xy=x^2+y^2-\left(x-y\right)^2=15-5^2=-10\)

=>xy=-5

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

\(=5^3+3\cdot\left(-5\right)\cdot5=125-75=50\)

2: \(N=a^2-6ab+9b^2-a^2-6ab-9b^2-ab+2a+b-2\)

\(=-13ab+2a+b-2\)

\(=-13\cdot\dfrac{1}{2}\cdot\left(-3\right)+2\cdot\dfrac{1}{2}+\left(-3\right)-2\)

\(=\dfrac{39}{2}+1-3-2=\dfrac{39}{2}-4=\dfrac{31}{2}\)

3: \(P=4x^2-25-4x^2-4x-1=-4x-26\)

=-8020-26=-8046

4: \(Q=\left(y^2-9\right)\left(y^2+9\right)-\left(y^2+2\right)\left(y^2-2\right)\)

\(=y^4-81-y^4+4=-77\)