Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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