Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((q-14)(q-14)=(q-14)^2=q^2+\color{magenta}{2.q.(-14)}+(-14)^2=q^2\color{magenta}{-28q}+196\)
2. \((-6p^3-12q)(-6p^3-12q)=(-6p^3-12q)^2=(-6p^3)^2\color{magenta}{+2.(-6p^3).(-12q)}+(-12q)^2=36p^{6}\color{magenta}{+144p^3q}+144q^2\)
3. \((\color{blue}{b}\color{red}{-11})(\color{blue}{b}\color{red}{+11})=\color{blue}{b}^2-\color{red}{11}^2=b^2-121\)
4. \((-12x+12)^2=(-12x)^2+\color{magenta}{2.(-12x).12}+12^2=144x^2\color{magenta}{-288x}+144\)
5. \((-6q^2+9)(-6q^2+9)=(-6q^2+9)^2=(-6q^2)^2\color{magenta}{+2.(-6q^2).9}+9^2=36q^{4}\color{magenta}{-108q^2}+81\)
6. \((\color{blue}{-10y^2}\color{red}{-10})(\color{blue}{-10y^2}\color{red}{+10})=\color{blue}{(-10y^2)}^2-\color{red}{(-10)}^2=100y^{4}-100\)
7. \((\color{red}{-5b^4}\color{blue}{+14})(\color{red}{5b^4}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(5b^4)}^2=196-25b^{8}\)
8. \((\color{blue}{-13y^4}\color{red}{-11p})(\color{blue}{-13y^4}\color{red}{+11p})=\color{blue}{(-13y^4)}^2-\color{red}{(-11p)}^2=169y^{8}-121p^2\)
9. \((\color{red}{-8p^2}\color{blue}{+13})(\color{red}{8p^2}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(8p^2)}^2=169-64p^{4}\)
10. \((-3p^5-14)(-3p^5-14)=(-3p^5-14)^2=(-3p^5)^2\color{magenta}{+2.(-3p^5).(-14)}+(-14)^2=9p^{10}\color{magenta}{+84p^5}+196\)
11. \((7x^3+6q)^2=(7x^3)^2\color{magenta}{+2.(7x^3).(6q)}+(6q)^2=49x^{6}\color{magenta}{+84qx^3}+36q^2\)
12. \((\color{blue}{12b^5}\color{red}{-10y})(\color{blue}{12b^5}\color{red}{+10y})=\color{blue}{(12b^5)}^2-\color{red}{(-10y)}^2=144b^{10}-100y^2\)