Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-3q^5+5b)^2=(-3q^5)^2\color{magenta}{+2.(-3q^5).(5b)}+(5b)^2=9q^{10}\color{magenta}{-30bq^5}+25b^2\)
2. \((\color{blue}{8b^5}\color{red}{+q})(\color{blue}{8b^5}\color{red}{-q})=\color{blue}{(8b^5)}^2-\color{red}{(1q)}^2=64b^{10}-1q^2\)
3. \((\color{blue}{-5q}\color{red}{+2})(\color{blue}{-5q}\color{red}{-2})=\color{blue}{(-5q)}^2-\color{red}{(2)}^2=25q^2-4\)
4. \((\color{red}{13s^4}\color{blue}{-6a})(\color{red}{-13s^4}\color{blue}{-6a})=\color{blue}{(-6a)}^2-\color{red}{(13s^4)}^2=36a^2-169s^{8}\)
5. \((\color{blue}{p}\color{red}{-2})(\color{blue}{p}\color{red}{+2})=\color{blue}{p}^2-\color{red}{2}^2=p^2-4\)
6. \((\color{blue}{-b^2}\color{red}{+8})(\color{blue}{-b^2}\color{red}{-8})=\color{blue}{(-b^2)}^2-\color{red}{8}^2=b^{4}-64\)
7. \((13a-10)(13a-10)=(13a-10)^2=(13a)^2+\color{magenta}{2.(13a).(-10)}+(-10)^2=169a^2\color{magenta}{-260a}+100\)
8. \((a+6)^2=a^2+\color{magenta}{2.a.6}+6^2=a^2\color{magenta}{+12a}+36\)
9. \((15a^3+2)^2=(15a^3)^2\color{magenta}{+2.(15a^3).2}+2^2=225a^{6}\color{magenta}{+60a^3}+4\)
10. \((\color{red}{-7b^3}\color{blue}{-11})(\color{red}{7b^3}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(7b^3)}^2=121-49b^{6}\)
11. \((11q+5)(11q+5)=(11q+5)^2=(11q)^2+\color{magenta}{2.(11q).5}+5^2=121q^2\color{magenta}{+110q}+25\)
12. \((q+1)^2=q^2+\color{magenta}{2.q.1}+1^2=q^2\color{magenta}{+2q}+1\)