Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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