Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((3q^3-13y)(3q^3-13y)=(3q^3-13y)^2=(3q^3)^2\color{magenta}{+2.(3q^3).(-13y)}+(-13y)^2=9q^{6}\color{magenta}{-78q^3y}+169y^2\)
2. \((\color{blue}{-13q^5}\color{red}{-10})(\color{blue}{-13q^5}\color{red}{+10})=\color{blue}{(-13q^5)}^2-\color{red}{(-10)}^2=169q^{10}-100\)
3. \((\color{blue}{s}\color{red}{+11})(\color{blue}{s}\color{red}{-11})=\color{blue}{s}^2-\color{red}{11}^2=s^2-121\)
4. \((\color{blue}{a^5}\color{red}{-1})(\color{blue}{a^5}\color{red}{+1})=\color{blue}{(a^5)}^2-\color{red}{(-1)}^2=a^{10}-1\)
5. \((4q^2+9y)^2=(4q^2)^2\color{magenta}{+2.(4q^2).(9y)}+(9y)^2=16q^{4}\color{magenta}{+72q^2y}+81y^2\)
6. \((14a^4-6q)^2=(14a^4)^2\color{magenta}{+2.(14a^4).(-6q)}+(-6q)^2=196a^{8}\color{magenta}{-168a^4q}+36q^2\)
7. \((\color{red}{-14s}\color{blue}{-10})(\color{red}{14s}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(14s)}^2=100-196s^2\)
8. \((-11q^3-13b)^2=(-11q^3)^2\color{magenta}{+2.(-11q^3).(-13b)}+(-13b)^2=121q^{6}\color{magenta}{+286bq^3}+169b^2\)
9. \((\color{blue}{11s^4}\color{red}{+8})(\color{blue}{11s^4}\color{red}{-8})=\color{blue}{(11s^4)}^2-\color{red}{8}^2=121s^{8}-64\)
10. \((-6q+8)^2=(-6q)^2+\color{magenta}{2.(-6q).8}+8^2=36q^2\color{magenta}{-96q}+64\)
11. \((\color{blue}{x}\color{red}{+13})(\color{blue}{x}\color{red}{-13})=\color{blue}{(x)}^2-\color{red}{(13)}^2=x^2-169\)
12. \((p+4)^2=p^2+\color{magenta}{2.p.4}+4^2=p^2\color{magenta}{+8p}+16\)