Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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