Lettervormen herleiden

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Herleid de lettervormen

1. \(xy-y-xy-2y+2xy\)
2. \(-4x-3x^2-2x\)
3. \(3p-3p^2-p\)
4. \(-2p-2q-2p-2q\)
5. \(2x-xy-x-xy\)
6. \(-2xy-y-3xy-4y\)
7. \(-4y-5y^2-y\)
8. \(-2a+b+3a-3b-a\)
9. \(2x-2y+4x-3y\)
10. \(x-3xy-3x+3xy+2x\)
11. \(-x+3y-3x+y+2x\)
12. \(-xy+2y+xy+y+xy\)

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Herleid de lettervormen

Verbetersleutel

1. \(\begin{align}xy-y-xy-2y+2xy&=1.xy-1.y-1.xy-2.y+2.xy\\&=1.xy-1.xy+2.xy-1.y-2.y\\&=2xy-3y\\\\ \end{align}\)
2. \(\begin{align} -4x-3x^2-2x&=-4.x-3.x^2-2.x\\&=-4.x-2.x-3.x^2\\&=-6x-3x^2\\\\ \end{align}\)
3. \(\begin{align} 3p-3p^2-p&=3.p-3.p^2-1.p\\&=3.p-1.p-3.p^2\\&=2p-3p^2\\\\ \end{align}\)
4. \(\begin{align}-2p-2q-2p-2q&=-2.p-2.q-2.p-2.q\\&=-2.p-2.p-2.q-2.q\\&=-4p-4q\\\\ \end{align}\)
5. \(\begin{align}2x-xy-x-xy&=2.x-1.xy-1.x-1.xy\\&=2.x-1.x-1.xy-1.xy\\&=x-2xy\\\\ \end{align}\)
6. \(\begin{align}-2xy-y-3xy-4y&=-2.xy-1.y-3.xy-4.y\\&=-2.xy-3.xy-1.y-4.y\\&=-5xy-5y\\\\ \end{align}\)
7. \(\begin{align} -4y-5y^2-y&=-4.y-5.y^2-1.y\\&=-4.y-1.y-5.y^2\\&=-5y-5y^2\\\\ \end{align}\)
8. \(\begin{align}-2a+b+3a-3b-a&=-2.a+1.b+3.a-3.b-1.a\\&=-2.a+3.a-1.a+1.b-3.b\\&=0a-2b\\&=-2b\\ \end{align}\)
9. \(\begin{align}2x-2y+4x-3y&=2.x-2.y+4.x-3.y\\&=2.x+4.x-2.y-3.y\\&=6x-5y\\\\ \end{align}\)
10. \(\begin{align}x-3xy-3x+3xy+2x&=1.x-3.xy-3.x+3.xy+2.x\\&=1.x-3.x+2.x-3.xy+3.xy\\&=0x+0xy\\&=0\\ \end{align}\)
11. \(\begin{align}-x+3y-3x+y+2x&=-1.x+3.y-3.x+1.y+2.x\\&=-1.x-3.x+2.x+3.y+1.y\\&=-2x+4y\\\\ \end{align}\)
12. \(\begin{align}-xy+2y+xy+y+xy&=-1.xy+2.y+1.xy+1.y+1.xy\\&=-1.xy+1.xy+1.xy+2.y+1.y\\&=xy+3y\\\\ \end{align}\)