Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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