Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{9y}\color{blue}{-6})(\color{red}{-9y}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(9y)}^2=36-81y^2\)
2. \((\color{blue}{p}\color{red}{-14})(\color{blue}{p}\color{red}{+14})=\color{blue}{p}^2-\color{red}{14}^2=p^2-196\)
3. \((\color{blue}{s}\color{red}{-13})(\color{blue}{s}\color{red}{+13})=\color{blue}{s}^2-\color{red}{13}^2=s^2-169\)
4. \((\color{blue}{16y^2}\color{red}{-10})(\color{blue}{16y^2}\color{red}{+10})=\color{blue}{(16y^2)}^2-\color{red}{(-10)}^2=256y^{4}-100\)
5. \((6x^4+3)(6x^4+3)=(6x^4+3)^2=(6x^4)^2\color{magenta}{+2.(6x^4).3}+3^2=36x^{8}\color{magenta}{+36x^4}+9\)
6. \((s-6)^2=s^2+\color{magenta}{2.s.(-6)}+(-6)^2=s^2\color{magenta}{-12s}+36\)
7. \((\color{red}{-9q^4}\color{blue}{-10})(\color{red}{9q^4}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(9q^4)}^2=100-81q^{8}\)
8. \((\color{blue}{-10a}\color{red}{+8})(\color{blue}{-10a}\color{red}{-8})=\color{blue}{(-10a)}^2-\color{red}{(8)}^2=100a^2-64\)
9. \((x-13)(x-13)=(x-13)^2=x^2+\color{magenta}{2.x.(-13)}+(-13)^2=x^2\color{magenta}{-26x}+169\)
10. \((\color{red}{-6b}\color{blue}{+5})(\color{red}{6b}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(6b)}^2=25-36b^2\)
11. \((\color{blue}{s}\color{red}{+14})(\color{blue}{s}\color{red}{-14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
12. \((4b-9)^2=(4b)^2+\color{magenta}{2.(4b).(-9)}+(-9)^2=16b^2\color{magenta}{-72b}+81\)