Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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