Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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