Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{-8})(\color{blue}{p}\color{red}{+8})=\color{blue}{p}^2-\color{red}{8}^2=p^2-64\)
2. \((\color{blue}{y}\color{red}{+13})(\color{blue}{y}\color{red}{-13})=\color{blue}{y}^2-\color{red}{13}^2=y^2-169\)
3. \((p+6)(p+6)=(p+6)^2=p^2+\color{magenta}{2.p.6}+6^2=p^2\color{magenta}{+12p}+36\)
4. \((\color{red}{-2x^3}\color{blue}{-4})(\color{red}{2x^3}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(2x^3)}^2=16-4x^{6}\)
5. \((\color{blue}{13x^2}\color{red}{+6})(\color{blue}{13x^2}\color{red}{-6})=\color{blue}{(13x^2)}^2-\color{red}{6}^2=169x^{4}-36\)
6. \((b+3)^2=b^2+\color{magenta}{2.b.3}+3^2=b^2\color{magenta}{+6b}+9\)
7. \((\color{blue}{p}\color{red}{-6})(\color{blue}{p}\color{red}{+6})=\color{blue}{p}^2-\color{red}{6}^2=p^2-36\)
8. \((\color{red}{-6q^4}\color{blue}{-10})(\color{red}{6q^4}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(6q^4)}^2=100-36q^{8}\)
9. \((\color{blue}{p}\color{red}{-14})(\color{blue}{p}\color{red}{+14})=\color{blue}{p}^2-\color{red}{14}^2=p^2-196\)
10. \((-8p^2-7s)^2=(-8p^2)^2\color{magenta}{+2.(-8p^2).(-7s)}+(-7s)^2=64p^{4}\color{magenta}{+112p^2s}+49s^2\)
11. \((\color{red}{13x^4}\color{blue}{+3})(\color{red}{-13x^4}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(13x^4)}^2=9-169x^{8}\)
12. \((\color{red}{12b^5}\color{blue}{+3y})(\color{red}{-12b^5}\color{blue}{+3y})=\color{blue}{(3y)}^2-\color{red}{(12b^5)}^2=9y^2-144b^{10}\)