Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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