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a, \(7x^2-14xy^2+7y^4=7\left(x^2-2xy^2+y^4\right)=7\left(x-y^2\right)^2\)
\(7.\left(x^2-2.x.y^2+y^4\right)\) \(=7.\left(x-y^2\right)^2\)
\(x^2+4x+4-y^2\) \(=\left(x^2+2.x.2+2^2\right)-y^2\) \(=\left(x+2\right)^2-y^2\) \(\left(x+2+y\right)\left(x+2-y\right)\)
a) \(x^2+7x+7y-y^2\)
\(=\left(x+y\right)\left(x-y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
b) \(x^2-xy-6y^2\)
\(=-6y^2-3xy+2xy+x^2\)
\(=-3y\left(2y+x\right)+x\left(2y+x\right)\)
\(=\left(x-3y\right)\left(2y+x\right)\)
c) \(x^2-3x^2-6x+8\)
\(=\left(x+2\right)\left(x^2-2x+4\right)-3x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-5x+4\right)\)
\(=\left(x+2\right)\left(x^2-4x-x+4\right)\)
\(=\left(x+2\right)\left[x\left(x-4\right)-\left(x-4\right)\right]\)
\(=\left(x+2\right)\left(x-1\right)\left(x-4\right)\)
a)x2+7x+7y-y2=(x-y)(x+y)+7.(x+y)
=(x+y)(x-y+7)
b)x2-xy-6y2=x2-xy-4y2-2y2
=(x-2y)(x+2y)-y(x-2y)
=(x-2y)(x+2y-y)
Ta có: \(xy=2\Rightarrow2xy=4\)
\(x+y=3\Rightarrow\left(x+y\right)^2=9\Rightarrow x^2+2xy+y^2=9\)
\(\Rightarrow x^2+y^2=5\text{ vì }2xy=4\)
\(x^3+y^3=\left(x+y\right)^3-3xy.\left(x+y\right)=\left(x+y\right).\left(x^2-xy+y^2\right)\)
\(\Rightarrow x^3+y^3+7x^2+7y^2=\left(x+y\right).\left(x^2-xy+y^2\right)+7.\left(x^2+y^2\right)\)
\(=3.\left(5-2\right)+7.5=9+35=44\)
Nếu câu hỏi là phân tích đa thức thành nhân tử:
\(7x^2-14xy^2-7y^4=7\left(x^2-2xy^2-\left(y^2\right)^2\right)=7\left(x-y^2\right)^2\)
Phan h da thuc thanh nhan tu a ban ?
Ta co
7x2-14xy+7y2
=7(x2-2xy+y2)
=7(x-y)2
Ta có:\(7x^2-14xy+7y^2\)
\(=7\left(x^2-2xy+y^2\right)\)
\(=7\left(x^2-2.x.y+y^2\right)\)
\(=7\left(x-y\right)^2\)