Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{10q}\color{blue}{+11})(\color{red}{-10q}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(10q)}^2=121-100q^2\)
2. \((-9a^3-12)^2=(-9a^3)^2\color{magenta}{+2.(-9a^3).(-12)}+(-12)^2=81a^{6}\color{magenta}{+216a^3}+144\)
3. \((5p^5-11x)^2=(5p^5)^2\color{magenta}{+2.(5p^5).(-11x)}+(-11x)^2=25p^{10}\color{magenta}{-110p^5x}+121x^2\)
4. \((6a+2)^2=(6a)^2+\color{magenta}{2.(6a).2}+2^2=36a^2\color{magenta}{+24a}+4\)
5. \((-8b^2+12a)^2=(-8b^2)^2\color{magenta}{+2.(-8b^2).(12a)}+(12a)^2=64b^{4}\color{magenta}{-192ab^2}+144a^2\)
6. \((\color{red}{-11x^3}\color{blue}{-5s})(\color{red}{11x^3}\color{blue}{-5s})=\color{blue}{(-5s)}^2-\color{red}{(11x^3)}^2=25s^2-121x^{6}\)
7. \((x-2)^2=x^2+\color{magenta}{2.x.(-2)}+(-2)^2=x^2\color{magenta}{-4x}+4\)
8. \((s+3)^2=s^2+\color{magenta}{2.s.3}+3^2=s^2\color{magenta}{+6s}+9\)
9. \((-y^4-8a)(-y^4-8a)=(-y^4-8a)^2=(-y^4)^2\color{magenta}{+2.(-y^4).(-8a)}+(-8a)^2=y^{8}\color{magenta}{+16ay^4}+64a^2\)
10. \((\color{blue}{12q}\color{red}{-9})(\color{blue}{12q}\color{red}{+9})=\color{blue}{(12q)}^2-\color{red}{(-9)}^2=144q^2-81\)
11. \((10a+3)(10a+3)=(10a+3)^2=(10a)^2+\color{magenta}{2.(10a).3}+3^2=100a^2\color{magenta}{+60a}+9\)
12. \((\color{blue}{s}\color{red}{-5})(\color{blue}{s}\color{red}{+5})=\color{blue}{s}^2-\color{red}{5}^2=s^2-25\)