Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{2s}\color{blue}{+5})(\color{red}{-2s}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(2s)}^2=25-4s^2\)
2. \((-8a^2-11)(-8a^2-11)=(-8a^2-11)^2=(-8a^2)^2\color{magenta}{+2.(-8a^2).(-11)}+(-11)^2=64a^{4}\color{magenta}{+176a^2}+121\)
3. \((\color{blue}{-y^3}\color{red}{-10s})(\color{blue}{-y^3}\color{red}{+10s})=\color{blue}{(-y^3)}^2-\color{red}{(-10s)}^2=y^{6}-100s^2\)
4. \((14b-7)^2=(14b)^2+\color{magenta}{2.(14b).(-7)}+(-7)^2=196b^2\color{magenta}{-196b}+49\)
5. \((\color{red}{14s}\color{blue}{+13})(\color{red}{-14s}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(14s)}^2=169-196s^2\)
6. \((\color{blue}{y}\color{red}{-7})(\color{blue}{y}\color{red}{+7})=\color{blue}{y}^2-\color{red}{7}^2=y^2-49\)
7. \((\color{red}{13y^5}\color{blue}{-6})(\color{red}{-13y^5}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(13y^5)}^2=36-169y^{10}\)
8. \((\color{blue}{-10s}\color{red}{-12})(\color{blue}{-10s}\color{red}{+12})=\color{blue}{(-10s)}^2-\color{red}{(-12)}^2=100s^2-144\)
9. \((15s-13)(15s-13)=(15s-13)^2=(15s)^2+\color{magenta}{2.(15s).(-13)}+(-13)^2=225s^2\color{magenta}{-390s}+169\)
10. \((\color{blue}{p}\color{red}{+13})(\color{blue}{p}\color{red}{-13})=\color{blue}{p}^2-\color{red}{13}^2=p^2-169\)
11. \((-11x^2+9b)(-11x^2+9b)=(-11x^2+9b)^2=(-11x^2)^2\color{magenta}{+2.(-11x^2).(9b)}+(9b)^2=121x^{4}\color{magenta}{-198bx^2}+81b^2\)
12. \((-8p^2+6)^2=(-8p^2)^2\color{magenta}{+2.(-8p^2).6}+6^2=64p^{4}\color{magenta}{-96p^2}+36\)