Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{+1})(\color{blue}{p}\color{red}{-1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
2. \((-13a^4-16)^2=(-13a^4)^2\color{magenta}{+2.(-13a^4).(-16)}+(-16)^2=169a^{8}\color{magenta}{+416a^4}+256\)
3. \((\color{red}{-15q^3}\color{blue}{+3p})(\color{red}{15q^3}\color{blue}{+3p})=\color{blue}{(3p)}^2-\color{red}{(15q^3)}^2=9p^2-225q^{6}\)
4. \((\color{blue}{5s^4}\color{red}{-2q})(\color{blue}{5s^4}\color{red}{+2q})=\color{blue}{(5s^4)}^2-\color{red}{(-2q)}^2=25s^{8}-4q^2\)
5. \((\color{blue}{y}\color{red}{-5})(\color{blue}{y}\color{red}{+5})=\color{blue}{y}^2-\color{red}{5}^2=y^2-25\)
6. \((\color{blue}{x}\color{red}{-13})(\color{blue}{x}\color{red}{+13})=\color{blue}{x}^2-\color{red}{13}^2=x^2-169\)
7. \((\color{blue}{b}\color{red}{+8})(\color{blue}{b}\color{red}{-8})=\color{blue}{b}^2-\color{red}{8}^2=b^2-64\)
8. \((\color{blue}{6p}\color{red}{+3})(\color{blue}{6p}\color{red}{-3})=\color{blue}{(6p)}^2-\color{red}{(3)}^2=36p^2-9\)
9. \((\color{blue}{b}\color{red}{-2})(\color{blue}{b}\color{red}{+2})=\color{blue}{b}^2-\color{red}{2}^2=b^2-4\)
10. \((a-8)^2=a^2+\color{magenta}{2.a.(-8)}+(-8)^2=a^2\color{magenta}{-16a}+64\)
11. \((\color{red}{16b^4}\color{blue}{-1})(\color{red}{-16b^4}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(16b^4)}^2=1-256b^{8}\)
12. \((\color{red}{-3s}\color{blue}{-8})(\color{red}{3s}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(3s)}^2=64-9s^2\)