Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-4b^4-14p)(-4b^4+14p)\)
2. \((3b+12)(-3b+12)\)
3. \((-3a-16)(-3a-16)\)
4. \((p-1)(p-1)\)
5. \((4a^5-5)(-4a^5-5)\)
6. \((s-9)(s-9)\)
7. \((-15p-13)^2\)
8. \((-6q^2+7p)(-6q^2-7p)\)
9. \((s-10)^2\)
10. \((x-11)^2\)
11. \((14p^5+3s)^2\)
12. \((15s^3+7q)(15s^3+7q)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-4b^4}\color{red}{-14p})(\color{blue}{-4b^4}\color{red}{+14p})=\color{blue}{(-4b^4)}^2-\color{red}{(-14p)}^2=16b^{8}-196p^2\)
2. \((\color{red}{3b}\color{blue}{+12})(\color{red}{-3b}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(3b)}^2=144-9b^2\)
3. \((-3a-16)(-3a-16)=(-3a-16)^2=(-3a)^2+\color{magenta}{2.(-3a).(-16)}+(-16)^2=9a^2\color{magenta}{+96a}+256\)
4. \((p-1)(p-1)=(p-1)^2=p^2+\color{magenta}{2.p.(-1)}+(-1)^2=p^2\color{magenta}{-2p}+1\)
5. \((\color{red}{4a^5}\color{blue}{-5})(\color{red}{-4a^5}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(4a^5)}^2=25-16a^{10}\)
6. \((s-9)(s-9)=(s-9)^2=s^2+\color{magenta}{2.s.(-9)}+(-9)^2=s^2\color{magenta}{-18s}+81\)
7. \((-15p-13)^2=(-15p)^2+\color{magenta}{2.(-15p).(-13)}+(-13)^2=225p^2\color{magenta}{+390p}+169\)
8. \((\color{blue}{-6q^2}\color{red}{+7p})(\color{blue}{-6q^2}\color{red}{-7p})=\color{blue}{(-6q^2)}^2-\color{red}{(7p)}^2=36q^{4}-49p^2\)
9. \((s-10)^2=s^2+\color{magenta}{2.s.(-10)}+(-10)^2=s^2\color{magenta}{-20s}+100\)
10. \((x-11)^2=x^2+\color{magenta}{2.x.(-11)}+(-11)^2=x^2\color{magenta}{-22x}+121\)
11. \((14p^5+3s)^2=(14p^5)^2\color{magenta}{+2.(14p^5).(3s)}+(3s)^2=196p^{10}\color{magenta}{+84p^5s}+9s^2\)
12. \((15s^3+7q)(15s^3+7q)=(15s^3+7q)^2=(15s^3)^2\color{magenta}{+2.(15s^3).(7q)}+(7q)^2=225s^{6}\color{magenta}{+210qs^3}+49q^2\)