Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-2x^2-15a)^2=(-2x^2)^2\color{magenta}{+2.(-2x^2).(-15a)}+(-15a)^2=4x^{4}\color{magenta}{+60ax^2}+225a^2\)
2. \((\color{blue}{s}\color{red}{-4})(\color{blue}{s}\color{red}{+4})=\color{blue}{s}^2-\color{red}{4}^2=s^2-16\)
3. \((p+14)^2=p^2+\color{magenta}{2.p.14}+14^2=p^2\color{magenta}{+28p}+196\)
4. \((\color{blue}{-6s^2}\color{red}{+10})(\color{blue}{-6s^2}\color{red}{-10})=\color{blue}{(-6s^2)}^2-\color{red}{10}^2=36s^{4}-100\)
5. \((s+10)^2=s^2+\color{magenta}{2.s.10}+10^2=s^2\color{magenta}{+20s}+100\)
6. \((-16p^3+7b)(-16p^3+7b)=(-16p^3+7b)^2=(-16p^3)^2\color{magenta}{+2.(-16p^3).(7b)}+(7b)^2=256p^{6}\color{magenta}{-224bp^3}+49b^2\)
7. \((\color{red}{b^5}\color{blue}{-12q})(\color{red}{-b^5}\color{blue}{-12q})=\color{blue}{(-12q)}^2-\color{red}{(b^5)}^2=144q^2-b^{10}\)
8. \((p+8)(p+8)=(p+8)^2=p^2+\color{magenta}{2.p.8}+8^2=p^2\color{magenta}{+16p}+64\)
9. \((4q^5+13s)^2=(4q^5)^2\color{magenta}{+2.(4q^5).(13s)}+(13s)^2=16q^{10}\color{magenta}{+104q^5s}+169s^2\)
10. \((\color{blue}{p}\color{red}{-8})(\color{blue}{p}\color{red}{+8})=\color{blue}{p}^2-\color{red}{8}^2=p^2-64\)
11. \((\color{blue}{11q^4}\color{red}{-9})(\color{blue}{11q^4}\color{red}{+9})=\color{blue}{(11q^4)}^2-\color{red}{(-9)}^2=121q^{8}-81\)
12. \((7b^5+11)^2=(7b^5)^2\color{magenta}{+2.(7b^5).11}+11^2=49b^{10}\color{magenta}{+154b^5}+121\)