Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-11b^3-12a)(-11b^3-12a)=(-11b^3-12a)^2=(-11b^3)^2\color{magenta}{+2.(-11b^3).(-12a)}+(-12a)^2=121b^{6}\color{magenta}{+264ab^3}+144a^2\)
2. \((\color{red}{-12s}\color{blue}{-13})(\color{red}{12s}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(12s)}^2=169-144s^2\)
3. \((p+3)^2=p^2+\color{magenta}{2.p.3}+3^2=p^2\color{magenta}{+6p}+9\)
4. \((\color{red}{-4q^3}\color{blue}{+7})(\color{red}{4q^3}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(4q^3)}^2=49-16q^{6}\)
5. \((\color{blue}{15y}\color{red}{+3})(\color{blue}{15y}\color{red}{-3})=\color{blue}{(15y)}^2-\color{red}{(3)}^2=225y^2-9\)
6. \((\color{blue}{s}\color{red}{+14})(\color{blue}{s}\color{red}{-14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
7. \((-2y^3+12)^2=(-2y^3)^2\color{magenta}{+2.(-2y^3).12}+12^2=4y^{6}\color{magenta}{-48y^3}+144\)
8. \((\color{blue}{2y^5}\color{red}{+7})(\color{blue}{2y^5}\color{red}{-7})=\color{blue}{(2y^5)}^2-\color{red}{7}^2=4y^{10}-49\)
9. \((\color{blue}{2q^4}\color{red}{+16})(\color{blue}{2q^4}\color{red}{-16})=\color{blue}{(2q^4)}^2-\color{red}{16}^2=4q^{8}-256\)
10. \((\color{red}{-p^4}\color{blue}{-11})(\color{red}{p^4}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(p^4)}^2=121-p^{8}\)
11. \((6s^3-15b)(6s^3-15b)=(6s^3-15b)^2=(6s^3)^2\color{magenta}{+2.(6s^3).(-15b)}+(-15b)^2=36s^{6}\color{magenta}{-180bs^3}+225b^2\)
12. \((\color{red}{-3s}\color{blue}{+16})(\color{red}{3s}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(3s)}^2=256-9s^2\)