Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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