Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-9b^2}\color{blue}{-9})(\color{red}{9b^2}\color{blue}{-9})=\color{blue}{(-9)}^2-\color{red}{(9b^2)}^2=81-81b^{4}\)
2. \((\color{blue}{s}\color{red}{+1})(\color{blue}{s}\color{red}{-1})=\color{blue}{s}^2-\color{red}{1}^2=s^2-1\)
3. \((\color{blue}{a}\color{red}{+7})(\color{blue}{a}\color{red}{-7})=\color{blue}{a}^2-\color{red}{7}^2=a^2-49\)
4. \((\color{blue}{13q^2}\color{red}{+13})(\color{blue}{13q^2}\color{red}{-13})=\color{blue}{(13q^2)}^2-\color{red}{13}^2=169q^{4}-169\)
5. \((\color{blue}{-2p^4}\color{red}{-3})(\color{blue}{-2p^4}\color{red}{+3})=\color{blue}{(-2p^4)}^2-\color{red}{(-3)}^2=4p^{8}-9\)
6. \((-3s+5)^2=(-3s)^2+\color{magenta}{2.(-3s).5}+5^2=9s^2\color{magenta}{-30s}+25\)
7. \((\color{red}{-15y}\color{blue}{+14})(\color{red}{15y}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(15y)}^2=196-225y^2\)
8. \((7s^2+1)(7s^2+1)=(7s^2+1)^2=(7s^2)^2\color{magenta}{+2.(7s^2).1}+1^2=49s^{4}\color{magenta}{+14s^2}+1\)
9. \((12b^3-13)(12b^3-13)=(12b^3-13)^2=(12b^3)^2\color{magenta}{+2.(12b^3).(-13)}+(-13)^2=144b^{6}\color{magenta}{-312b^3}+169\)
10. \((-7p^5+5)(-7p^5+5)=(-7p^5+5)^2=(-7p^5)^2\color{magenta}{+2.(-7p^5).5}+5^2=49p^{10}\color{magenta}{-70p^5}+25\)
11. \((\color{red}{-9y}\color{blue}{-4})(\color{red}{9y}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(9y)}^2=16-81y^2\)
12. \((\color{blue}{14b}\color{red}{+1})(\color{blue}{14b}\color{red}{-1})=\color{blue}{(14b)}^2-\color{red}{(1)}^2=196b^2-1\)