Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-11x^2}\color{red}{-11a})(\color{blue}{-11x^2}\color{red}{+11a})=\color{blue}{(-11x^2)}^2-\color{red}{(-11a)}^2=121x^{4}-121a^2\)
2. \((-14x^2-1)(-14x^2-1)=(-14x^2-1)^2=(-14x^2)^2\color{magenta}{+2.(-14x^2).(-1)}+(-1)^2=196x^{4}\color{magenta}{+28x^2}+1\)
3. \((-9y+6)^2=(-9y)^2+\color{magenta}{2.(-9y).6}+6^2=81y^2\color{magenta}{-108y}+36\)
4. \((\color{red}{-13q^3}\color{blue}{+14x})(\color{red}{13q^3}\color{blue}{+14x})=\color{blue}{(14x)}^2-\color{red}{(13q^3)}^2=196x^2-169q^{6}\)
5. \((\color{blue}{-5p}\color{red}{-11})(\color{blue}{-5p}\color{red}{+11})=\color{blue}{(-5p)}^2-\color{red}{(-11)}^2=25p^2-121\)
6. \((a-12)(a-12)=(a-12)^2=a^2+\color{magenta}{2.a.(-12)}+(-12)^2=a^2\color{magenta}{-24a}+144\)
7. \((\color{blue}{x}\color{red}{-13})(\color{blue}{x}\color{red}{+13})=\color{blue}{x}^2-\color{red}{13}^2=x^2-169\)
8. \((\color{red}{10y}\color{blue}{-1})(\color{red}{-10y}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(10y)}^2=1-100y^2\)
9. \((\color{blue}{b}\color{red}{-9})(\color{blue}{b}\color{red}{+9})=\color{blue}{b}^2-\color{red}{9}^2=b^2-81\)
10. \((y-14)^2=y^2+\color{magenta}{2.y.(-14)}+(-14)^2=y^2\color{magenta}{-28y}+196\)
11. \((\color{blue}{p}\color{red}{+2})(\color{blue}{p}\color{red}{-2})=\color{blue}{p}^2-\color{red}{2}^2=p^2-4\)
12. \((\color{blue}{b}\color{red}{+12})(\color{blue}{b}\color{red}{-12})=\color{blue}{b}^2-\color{red}{12}^2=b^2-144\)