Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{5b^5}\color{blue}{+5})(\color{red}{-5b^5}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(5b^5)}^2=25-25b^{10}\)
2. \((\color{red}{-11s^4}\color{blue}{-6})(\color{red}{11s^4}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(11s^4)}^2=36-121s^{8}\)
3. \((4b+10)(4b+10)=(4b+10)^2=(4b)^2+\color{magenta}{2.(4b).10}+10^2=16b^2\color{magenta}{+80b}+100\)
4. \((\color{blue}{-7y^5}\color{red}{+4s})(\color{blue}{-7y^5}\color{red}{-4s})=\color{blue}{(-7y^5)}^2-\color{red}{(4s)}^2=49y^{10}-16s^2\)
5. \((\color{red}{14b}\color{blue}{-6})(\color{red}{-14b}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(14b)}^2=36-196b^2\)
6. \((\color{blue}{s}\color{red}{-11})(\color{blue}{s}\color{red}{+11})=\color{blue}{s}^2-\color{red}{11}^2=s^2-121\)
7. \((\color{red}{11s^2}\color{blue}{+3})(\color{red}{-11s^2}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(11s^2)}^2=9-121s^{4}\)
8. \((\color{blue}{q}\color{red}{+10})(\color{blue}{q}\color{red}{-10})=\color{blue}{q}^2-\color{red}{10}^2=q^2-100\)
9. \((\color{blue}{y}\color{red}{-8})(\color{blue}{y}\color{red}{+8})=\color{blue}{y}^2-\color{red}{8}^2=y^2-64\)
10. \((\color{blue}{-8y}\color{red}{-5})(\color{blue}{-8y}\color{red}{+5})=\color{blue}{(-8y)}^2-\color{red}{(-5)}^2=64y^2-25\)
11. \((2a^5+16q)(2a^5+16q)=(2a^5+16q)^2=(2a^5)^2\color{magenta}{+2.(2a^5).(16q)}+(16q)^2=4a^{10}\color{magenta}{+64a^5q}+256q^2\)
12. \((8a+11)^2=(8a)^2+\color{magenta}{2.(8a).11}+11^2=64a^2\color{magenta}{+176a}+121\)