Lettervormen herleiden

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Herleid de lettervormen

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

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Herleid de lettervormen

Verbetersleutel

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