Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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