Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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