Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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