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\(M=x^3+y^3-2\left(x^2+y^2\right)+3xy\left(x+y\right)-4xy+3x+10+3y\)
\(=x^3+y^3-2x^2-2y^2+3x^2y+3xy^2-4xy+3x+10+3y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-2\left(x^2+2xy+y^2\right)+3\left(x+y\right)+10\)
\(=\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10\)
Ta có: x + y = 5
\(\Rightarrow\left(x+y\right)^3-2\left(x+y\right)^2+3\left(x+y\right)+10=5^3-2.5^2+3.5+10=125-50+15+10=100\)
Vậy M = 100.
1,Tính giá trị của biểu thức:
a,A=2.(x3-y3)-3.(x+y)2 với x-y=2
b,B=x3-3xy.(x-y)-y3-x2+2xy-y2 với x-y=7
\(P=\left(x-y\right)^2+\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)-4x^2=\left(x-y-x-y\right)^2-\left(2x\right)^2=\left(-2y\right)^2-\left(2x\right)^2\)
\(=\left(2y-2x\right)\left(2y+2x\right)=2\left(y-x\right)2\left(y+x\right)=4\left(x+y\right)\left(y-x\right)\)
\(x^3-x^2y+3x-3y=x^2\left(x-y\right)+3\left(x-y\right)=\left(x-y\right)\left(x^2+3\right)\)
\(x^3-2x^2-4xy^2+x=x\left(x^2-2x+1-4y^2\right)=x\left[\left(x-1\right)^2-\left(2y\right)^2\right]=x\left(x+2y-1\right)\left(x-2y-1\right)\)
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-8=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-8\)
Đặt \(x^2+7x+10=t\), ta có:
\(t\left(t+2\right)-8=t^2+2t-8=t^2-2t+4t-8=t\left(t-2\right)+4\left(t-2\right)=\left(t-2\right)\left(t+4\right)\)
\(=\left(x^2+7x+10+4\right)\left(x^2+7x+10-2\right)=\left(x^2+7x+14\right)\left(x^2+7x-8\right)\)
\(B=\left(x-y\right)^3-x^2+2xy-y^2=\left(x-y\right)^3-\left(x-y\right)^2\)
Thay x - y = -5 vào B ta có:
\(\left(-5\right)^3-\left(-5\right)^2=-125-25=-150\)
Ta có:
\(B=\left(x-y\right)^3-x^2+2xy-y^2\)
=\(\left(x-y\right)^3-\left(x^2-2xy+y^2\right)\)
=\(\left(x-y\right)^3-\left(x-y\right)^2\)
=\(\left(-5\right)^3-\left(-5\right)^2\) (do x-y=-5)
=\(-125-25=-150\)
Vậy...
\(a)\)\(M=x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2\) ( đề nhầm đúng ko bn )
\(M=\left(x^3-3x^2y+3xy^2-y^3\right)-\left(x^2-2xy+y^2\right)\)
\(M=\left(x-y\right)^3-\left(x-y\right)^2\)
\(M=7^3-7^2\)
\(M=294\)
Chúc bạn học tốt ~
a. Có \(x+y=2\Rightarrow x^2+2xy+y^2=4\Rightarrow x^2+y^2=4-2.\left(-3\right)=10\)
\(x^4+y^4=\left(x^2\right)^2+\left(y^2\right)^2=\left(x^2+y^2\right)^2-2x^2y^2\)
\(=10^2-2.\left(-3\right)^2=82\)
b. Ta có \(x+y=1\Rightarrow x^2+y^2=1-2xy\)
\(x^3+y^3+3xy=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\)
\(=1.\left(1-2xy-xy\right)+3xy=1\)
Các câu còn lại tương tự
\(K=x^3-3xy\left(x-y\right)-x^2+2xy-y^2\left(y+1\right)\)
\(=x^3-3x^2y+3xy^2-x^2+2xy-y^3-y^2\)
\(=\left(x^3-3x^2y+3xy^2-y^3\right)-\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)^3-\left(x-y\right)^2\)
Ta có: x - y = 7 \(\Rightarrow\left(x-y\right)^3-\left(x-y\right)^2=7^3-7^2=342-49=293\)
Vậy K = 293.
giỏi hề 7^3=342.