Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{s}\color{red}{+11})(\color{blue}{s}\color{red}{-11})=\color{blue}{s}^2-\color{red}{11}^2=s^2-121\)
2. \((\color{blue}{4q}\color{red}{+3})(\color{blue}{4q}\color{red}{-3})=\color{blue}{(4q)}^2-\color{red}{(3)}^2=16q^2-9\)
3. \((\color{blue}{9q^3}\color{red}{+15})(\color{blue}{9q^3}\color{red}{-15})=\color{blue}{(9q^3)}^2-\color{red}{15}^2=81q^{6}-225\)
4. \((\color{red}{-16x^5}\color{blue}{-8p})(\color{red}{16x^5}\color{blue}{-8p})=\color{blue}{(-8p)}^2-\color{red}{(16x^5)}^2=64p^2-256x^{10}\)
5. \((\color{blue}{x}\color{red}{+7})(\color{blue}{x}\color{red}{-7})=\color{blue}{x}^2-\color{red}{7}^2=x^2-49\)
6. \((\color{red}{-13x^5}\color{blue}{-6b})(\color{red}{13x^5}\color{blue}{-6b})=\color{blue}{(-6b)}^2-\color{red}{(13x^5)}^2=36b^2-169x^{10}\)
7. \((\color{blue}{-11s^2}\color{red}{-7b})(\color{blue}{-11s^2}\color{red}{+7b})=\color{blue}{(-11s^2)}^2-\color{red}{(-7b)}^2=121s^{4}-49b^2\)
8. \((5p^3+13)^2=(5p^3)^2\color{magenta}{+2.(5p^3).13}+13^2=25p^{6}\color{magenta}{+130p^3}+169\)
9. \((16a^2-11)(16a^2-11)=(16a^2-11)^2=(16a^2)^2\color{magenta}{+2.(16a^2).(-11)}+(-11)^2=256a^{4}\color{magenta}{-352a^2}+121\)
10. \((-11s^3-3y)^2=(-11s^3)^2\color{magenta}{+2.(-11s^3).(-3y)}+(-3y)^2=121s^{6}\color{magenta}{+66s^3y}+9y^2\)
11. \((\color{blue}{-6a^5}\color{red}{+3})(\color{blue}{-6a^5}\color{red}{-3})=\color{blue}{(-6a^5)}^2-\color{red}{3}^2=36a^{10}-9\)
12. \((\color{blue}{3y^2}\color{red}{-8})(\color{blue}{3y^2}\color{red}{+8})=\color{blue}{(3y^2)}^2-\color{red}{(-8)}^2=9y^{4}-64\)