Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-16p^4}\color{blue}{+7})(\color{red}{16p^4}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(16p^4)}^2=49-256p^{8}\)
2. \((\color{blue}{-9b^2}\color{red}{+4q})(\color{blue}{-9b^2}\color{red}{-4q})=\color{blue}{(-9b^2)}^2-\color{red}{(4q)}^2=81b^{4}-16q^2\)
3. \((15q^3-7)^2=(15q^3)^2\color{magenta}{+2.(15q^3).(-7)}+(-7)^2=225q^{6}\color{magenta}{-210q^3}+49\)
4. \((\color{blue}{-9x^3}\color{red}{-3})(\color{blue}{-9x^3}\color{red}{+3})=\color{blue}{(-9x^3)}^2-\color{red}{(-3)}^2=81x^{6}-9\)
5. \((\color{red}{-12q^3}\color{blue}{-5s})(\color{red}{12q^3}\color{blue}{-5s})=\color{blue}{(-5s)}^2-\color{red}{(12q^3)}^2=25s^2-144q^{6}\)
6. \((p-10)^2=p^2+\color{magenta}{2.p.(-10)}+(-10)^2=p^2\color{magenta}{-20p}+100\)
7. \((-7b-4)(-7b-4)=(-7b-4)^2=(-7b)^2+\color{magenta}{2.(-7b).(-4)}+(-4)^2=49b^2\color{magenta}{+56b}+16\)
8. \((y-13)^2=y^2+\color{magenta}{2.y.(-13)}+(-13)^2=y^2\color{magenta}{-26y}+169\)
9. \((x+9)^2=x^2+\color{magenta}{2.x.9}+9^2=x^2\color{magenta}{+18x}+81\)
10. \((-p^4-2)(-p^4-2)=(-p^4-2)^2=(-p^4)^2\color{magenta}{+2.(-p^4).(-2)}+(-2)^2=1p^{8}\color{magenta}{+4p^4}+4\)
11. \((x+14)^2=x^2+\color{magenta}{2.x.14}+14^2=x^2\color{magenta}{+28x}+196\)
12. \((-16q^2-16)(-16q^2-16)=(-16q^2-16)^2=(-16q^2)^2\color{magenta}{+2.(-16q^2).(-16)}+(-16)^2=256q^{4}\color{magenta}{+512q^2}+256\)