Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-p^2+2)(-p^2-2)\)
2. \((s-5)(s+5)\)
3. \((-10a+15)^2\)
4. \((-15b^5-12x)(15b^5-12x)\)
5. \((-2q^2-16)(2q^2-16)\)
6. \((y-11)^2\)
7. \((15x^5+13b)(15x^5-13b)\)
8. \((-11q-6)(-11q+6)\)
9. \((2y^2-2)(2y^2+2)\)
10. \((5s^3-11)(5s^3-11)\)
11. \((14p^5-16)(-14p^5-16)\)
12. \((-3q^2-5)(3q^2-5)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-p^2}\color{red}{+2})(\color{blue}{-p^2}\color{red}{-2})=\color{blue}{(-p^2)}^2-\color{red}{2}^2=p^{4}-4\)
2. \((\color{blue}{s}\color{red}{-5})(\color{blue}{s}\color{red}{+5})=\color{blue}{s}^2-\color{red}{5}^2=s^2-25\)
3. \((-10a+15)^2=(-10a)^2+\color{magenta}{2.(-10a).15}+15^2=100a^2\color{magenta}{-300a}+225\)
4. \((\color{red}{-15b^5}\color{blue}{-12x})(\color{red}{15b^5}\color{blue}{-12x})=\color{blue}{(-12x)}^2-\color{red}{(15b^5)}^2=144x^2-225b^{10}\)
5. \((\color{red}{-2q^2}\color{blue}{-16})(\color{red}{2q^2}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(2q^2)}^2=256-4q^{4}\)
6. \((y-11)^2=y^2+\color{magenta}{2.y.(-11)}+(-11)^2=y^2\color{magenta}{-22y}+121\)
7. \((\color{blue}{15x^5}\color{red}{+13b})(\color{blue}{15x^5}\color{red}{-13b})=\color{blue}{(15x^5)}^2-\color{red}{(13b)}^2=225x^{10}-169b^2\)
8. \((\color{blue}{-11q}\color{red}{-6})(\color{blue}{-11q}\color{red}{+6})=\color{blue}{(-11q)}^2-\color{red}{(-6)}^2=121q^2-36\)
9. \((\color{blue}{2y^2}\color{red}{-2})(\color{blue}{2y^2}\color{red}{+2})=\color{blue}{(2y^2)}^2-\color{red}{(-2)}^2=4y^{4}-4\)
10. \((5s^3-11)(5s^3-11)=(5s^3-11)^2=(5s^3)^2\color{magenta}{+2.(5s^3).(-11)}+(-11)^2=25s^{6}\color{magenta}{-110s^3}+121\)
11. \((\color{red}{14p^5}\color{blue}{-16})(\color{red}{-14p^5}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(14p^5)}^2=256-196p^{10}\)
12. \((\color{red}{-3q^2}\color{blue}{-5})(\color{red}{3q^2}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(3q^2)}^2=25-9q^{4}\)