Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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