Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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