Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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