Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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