Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-13p^3-14)(-13p^3-14)=(-13p^3-14)^2=(-13p^3)^2\color{magenta}{+2.(-13p^3).(-14)}+(-14)^2=169p^{6}\color{magenta}{+364p^3}+196\)
2. \((\color{blue}{2y^4}\color{red}{-4})(\color{blue}{2y^4}\color{red}{+4})=\color{blue}{(2y^4)}^2-\color{red}{(-4)}^2=4y^{8}-16\)
3. \((\color{blue}{-9y^5}\color{red}{+4})(\color{blue}{-9y^5}\color{red}{-4})=\color{blue}{(-9y^5)}^2-\color{red}{4}^2=81y^{10}-16\)
4. \((\color{red}{-4y}\color{blue}{-8})(\color{red}{4y}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(4y)}^2=64-16y^2\)
5. \((\color{red}{-13p^3}\color{blue}{-6})(\color{red}{13p^3}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(13p^3)}^2=36-169p^{6}\)
6. \((10y^2+9p)(10y^2+9p)=(10y^2+9p)^2=(10y^2)^2\color{magenta}{+2.(10y^2).(9p)}+(9p)^2=100y^{4}\color{magenta}{+180py^2}+81p^2\)
7. \((\color{blue}{p}\color{red}{-15})(\color{blue}{p}\color{red}{+15})=\color{blue}{(p)}^2-\color{red}{(-15)}^2=p^2-225\)
8. \((\color{blue}{13b^2}\color{red}{+13})(\color{blue}{13b^2}\color{red}{-13})=\color{blue}{(13b^2)}^2-\color{red}{13}^2=169b^{4}-169\)
9. \((\color{blue}{x}\color{red}{-12})(\color{blue}{x}\color{red}{+12})=\color{blue}{x}^2-\color{red}{12}^2=x^2-144\)
10. \((s-14)^2=s^2+\color{magenta}{2.s.(-14)}+(-14)^2=s^2\color{magenta}{-28s}+196\)
11. \((-3b^4-9)^2=(-3b^4)^2\color{magenta}{+2.(-3b^4).(-9)}+(-9)^2=9b^{8}\color{magenta}{+54b^4}+81\)
12. \((q-11)^2=q^2+\color{magenta}{2.q.(-11)}+(-11)^2=q^2\color{magenta}{-22q}+121\)