Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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