Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{11p^5}\color{red}{-9q})(\color{blue}{11p^5}\color{red}{+9q})=\color{blue}{(11p^5)}^2-\color{red}{(-9q)}^2=121p^{10}-81q^2\)
2. \((-3y^2-5s)^2=(-3y^2)^2\color{magenta}{+2.(-3y^2).(-5s)}+(-5s)^2=9y^{4}\color{magenta}{+30sy^2}+25s^2\)
3. \((\color{red}{12s^3}\color{blue}{+7})(\color{red}{-12s^3}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(12s^3)}^2=49-144s^{6}\)
4. \((s+4)(s+4)=(s+4)^2=s^2+\color{magenta}{2.s.4}+4^2=s^2\color{magenta}{+8s}+16\)
5. \((4s^4-14y)^2=(4s^4)^2\color{magenta}{+2.(4s^4).(-14y)}+(-14y)^2=16s^{8}\color{magenta}{-112s^4y}+196y^2\)
6. \((\color{blue}{p}\color{red}{+13})(\color{blue}{p}\color{red}{-13})=\color{blue}{p}^2-\color{red}{13}^2=p^2-169\)
7. \((15s^2-13)^2=(15s^2)^2\color{magenta}{+2.(15s^2).(-13)}+(-13)^2=225s^{4}\color{magenta}{-390s^2}+169\)
8. \((-14s^4+2b)(-14s^4+2b)=(-14s^4+2b)^2=(-14s^4)^2\color{magenta}{+2.(-14s^4).(2b)}+(2b)^2=196s^{8}\color{magenta}{-56bs^4}+4b^2\)
9. \((\color{blue}{s}\color{red}{+12})(\color{blue}{s}\color{red}{-12})=\color{blue}{s}^2-\color{red}{12}^2=s^2-144\)
10. \((4x^2-a)^2=(4x^2)^2\color{magenta}{+2.(4x^2).(-a)}+(-a)^2=16x^{4}\color{magenta}{-8ax^2}+1a^2\)
11. \((\color{blue}{x}\color{red}{+7})(\color{blue}{x}\color{red}{-7})=\color{blue}{x}^2-\color{red}{7}^2=x^2-49\)
12. \((\color{blue}{-12q^2}\color{red}{+4})(\color{blue}{-12q^2}\color{red}{-4})=\color{blue}{(-12q^2)}^2-\color{red}{4}^2=144q^{4}-16\)