Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((8s^4-7)(8s^4+7)\)
2. \((8q^5+9y)^2\)
3. \((13y^2-12p)^2\)
4. \((5x^2+11)(-5x^2+11)\)
5. \((s+14)(s-14)\)
6. \((-14y^5+9)(14y^5+9)\)
7. \((13q^4+16)(13q^4-16)\)
8. \((3x^4-4a)(-3x^4-4a)\)
9. \((y-3)(y+3)\)
10. \((-11q^3+9)(-11q^3-9)\)
11. \((-16s^4+10p)(16s^4+10p)\)
12. \((-5a-16)(-5a+16)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{8s^4}\color{red}{-7})(\color{blue}{8s^4}\color{red}{+7})=\color{blue}{(8s^4)}^2-\color{red}{(-7)}^2=64s^{8}-49\)
2. \((8q^5+9y)^2=(8q^5)^2\color{magenta}{+2.(8q^5).(9y)}+(9y)^2=64q^{10}\color{magenta}{+144q^5y}+81y^2\)
3. \((13y^2-12p)^2=(13y^2)^2\color{magenta}{+2.(13y^2).(-12p)}+(-12p)^2=169y^{4}\color{magenta}{-312py^2}+144p^2\)
4. \((\color{red}{5x^2}\color{blue}{+11})(\color{red}{-5x^2}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(5x^2)}^2=121-25x^{4}\)
5. \((\color{blue}{s}\color{red}{+14})(\color{blue}{s}\color{red}{-14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
6. \((\color{red}{-14y^5}\color{blue}{+9})(\color{red}{14y^5}\color{blue}{+9})=\color{blue}{9}^2-\color{red}{(14y^5)}^2=81-196y^{10}\)
7. \((\color{blue}{13q^4}\color{red}{+16})(\color{blue}{13q^4}\color{red}{-16})=\color{blue}{(13q^4)}^2-\color{red}{16}^2=169q^{8}-256\)
8. \((\color{red}{3x^4}\color{blue}{-4a})(\color{red}{-3x^4}\color{blue}{-4a})=\color{blue}{(-4a)}^2-\color{red}{(3x^4)}^2=16a^2-9x^{8}\)
9. \((\color{blue}{y}\color{red}{-3})(\color{blue}{y}\color{red}{+3})=\color{blue}{y}^2-\color{red}{3}^2=y^2-9\)
10. \((\color{blue}{-11q^3}\color{red}{+9})(\color{blue}{-11q^3}\color{red}{-9})=\color{blue}{(-11q^3)}^2-\color{red}{9}^2=121q^{6}-81\)
11. \((\color{red}{-16s^4}\color{blue}{+10p})(\color{red}{16s^4}\color{blue}{+10p})=\color{blue}{(10p)}^2-\color{red}{(16s^4)}^2=100p^2-256s^{8}\)
12. \((\color{blue}{-5a}\color{red}{-16})(\color{blue}{-5a}\color{red}{+16})=\color{blue}{(-5a)}^2-\color{red}{(-16)}^2=25a^2-256\)