Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((s+4)(s+4)=(s+4)^2=s^2+\color{magenta}{2.s.4}+4^2=s^2\color{magenta}{+8s}+16\)
2. \((\color{blue}{-11a}\color{red}{-13})(\color{blue}{-11a}\color{red}{+13})=\color{blue}{(-11a)}^2-\color{red}{(-13)}^2=121a^2-169\)
3. \((\color{blue}{-6y^2}\color{red}{-13})(\color{blue}{-6y^2}\color{red}{+13})=\color{blue}{(-6y^2)}^2-\color{red}{(-13)}^2=36y^{4}-169\)
4. \((\color{blue}{a}\color{red}{+9})(\color{blue}{a}\color{red}{-9})=\color{blue}{a}^2-\color{red}{9}^2=a^2-81\)
5. \((-10b^3+11y)^2=(-10b^3)^2\color{magenta}{+2.(-10b^3).(11y)}+(11y)^2=100b^{6}\color{magenta}{-220b^3y}+121y^2\)
6. \((\color{blue}{b}\color{red}{-3})(\color{blue}{b}\color{red}{+3})=\color{blue}{b}^2-\color{red}{3}^2=b^2-9\)
7. \((-6s^2+8)^2=(-6s^2)^2\color{magenta}{+2.(-6s^2).8}+8^2=36s^{4}\color{magenta}{-96s^2}+64\)
8. \((\color{blue}{7b^4}\color{red}{+10p})(\color{blue}{7b^4}\color{red}{-10p})=\color{blue}{(7b^4)}^2-\color{red}{(10p)}^2=49b^{8}-100p^2\)
9. \((\color{red}{13q^4}\color{blue}{-6s})(\color{red}{-13q^4}\color{blue}{-6s})=\color{blue}{(-6s)}^2-\color{red}{(13q^4)}^2=36s^2-169q^{8}\)
10. \((\color{blue}{-3p^2}\color{red}{-10})(\color{blue}{-3p^2}\color{red}{+10})=\color{blue}{(-3p^2)}^2-\color{red}{(-10)}^2=9p^{4}-100\)
11. \((\color{blue}{b}\color{red}{+5})(\color{blue}{b}\color{red}{-5})=\color{blue}{b}^2-\color{red}{5}^2=b^2-25\)
12. \((p+8)^2=p^2+\color{magenta}{2.p.8}+8^2=p^2\color{magenta}{+16p}+64\)