Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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