Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{+2})(\color{blue}{p}\color{red}{-2})=\color{blue}{p}^2-\color{red}{2}^2=p^2-4\)
2. \((\color{blue}{5q}\color{red}{-16})(\color{blue}{5q}\color{red}{+16})=\color{blue}{(5q)}^2-\color{red}{(-16)}^2=25q^2-256\)
3. \((-7x-6)^2=(-7x)^2+\color{magenta}{2.(-7x).(-6)}+(-6)^2=49x^2\color{magenta}{+84x}+36\)
4. \((-15x^3-7)(-15x^3-7)=(-15x^3-7)^2=(-15x^3)^2\color{magenta}{+2.(-15x^3).(-7)}+(-7)^2=225x^{6}\color{magenta}{+210x^3}+49\)
5. \((s-3)^2=s^2+\color{magenta}{2.s.(-3)}+(-3)^2=s^2\color{magenta}{-6s}+9\)
6. \((\color{blue}{16s^5}\color{red}{-1})(\color{blue}{16s^5}\color{red}{+1})=\color{blue}{(16s^5)}^2-\color{red}{(-1)}^2=256s^{10}-1\)
7. \((\color{red}{-3q^4}\color{blue}{+15x})(\color{red}{3q^4}\color{blue}{+15x})=\color{blue}{(15x)}^2-\color{red}{(3q^4)}^2=225x^2-9q^{8}\)
8. \((-6p^4-4)(-6p^4-4)=(-6p^4-4)^2=(-6p^4)^2\color{magenta}{+2.(-6p^4).(-4)}+(-4)^2=36p^{8}\color{magenta}{+48p^4}+16\)
9. \((\color{blue}{y}\color{red}{-12})(\color{blue}{y}\color{red}{+12})=\color{blue}{y}^2-\color{red}{12}^2=y^2-144\)
10. \((\color{red}{-14s}\color{blue}{-12})(\color{red}{14s}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(14s)}^2=144-196s^2\)
11. \((\color{blue}{-7p^2}\color{red}{+11a})(\color{blue}{-7p^2}\color{red}{-11a})=\color{blue}{(-7p^2)}^2-\color{red}{(11a)}^2=49p^{4}-121a^2\)
12. \((s+3)^2=s^2+\color{magenta}{2.s.3}+3^2=s^2\color{magenta}{+6s}+9\)