Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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