Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-13q^2}\color{blue}{+7s})(\color{red}{13q^2}\color{blue}{+7s})=\color{blue}{(7s)}^2-\color{red}{(13q^2)}^2=49s^2-169q^{4}\)
2. \((\color{blue}{b^4}\color{red}{-12})(\color{blue}{b^4}\color{red}{+12})=\color{blue}{(b^4)}^2-\color{red}{(-12)}^2=b^{8}-144\)
3. \((-p-12)^2=(-p)^2+\color{magenta}{2.(-p).(-12)}+(-12)^2=p^2\color{magenta}{+24p}+144\)
4. \((\color{red}{9a^4}\color{blue}{+13x})(\color{red}{-9a^4}\color{blue}{+13x})=\color{blue}{(13x)}^2-\color{red}{(9a^4)}^2=169x^2-81a^{8}\)
5. \((\color{blue}{6b^2}\color{red}{-14x})(\color{blue}{6b^2}\color{red}{+14x})=\color{blue}{(6b^2)}^2-\color{red}{(-14x)}^2=36b^{4}-196x^2\)
6. \((-13q-15)(-13q-15)=(-13q-15)^2=(-13q)^2+\color{magenta}{2.(-13q).(-15)}+(-15)^2=169q^2\color{magenta}{+390q}+225\)
7. \((\color{blue}{-15b^5}\color{red}{-5q})(\color{blue}{-15b^5}\color{red}{+5q})=\color{blue}{(-15b^5)}^2-\color{red}{(-5q)}^2=225b^{10}-25q^2\)
8. \((\color{red}{2b}\color{blue}{+3})(\color{red}{-2b}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(2b)}^2=9-4b^2\)
9. \((\color{blue}{-15s}\color{red}{+3})(\color{blue}{-15s}\color{red}{-3})=\color{blue}{(-15s)}^2-\color{red}{(3)}^2=225s^2-9\)
10. \((-14s-12)(-14s-12)=(-14s-12)^2=(-14s)^2+\color{magenta}{2.(-14s).(-12)}+(-12)^2=196s^2\color{magenta}{+336s}+144\)
11. \((\color{blue}{a}\color{red}{+14})(\color{blue}{a}\color{red}{-14})=\color{blue}{a}^2-\color{red}{14}^2=a^2-196\)
12. \((-13q^2+13b)(-13q^2+13b)=(-13q^2+13b)^2=(-13q^2)^2\color{magenta}{+2.(-13q^2).(13b)}+(13b)^2=169q^{4}\color{magenta}{-338bq^2}+169b^2\)