Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-5p}\color{red}{-2})(\color{blue}{-5p}\color{red}{+2})=\color{blue}{(-5p)}^2-\color{red}{(-2)}^2=25p^2-4\)
2. \((\color{red}{-8q}\color{blue}{+2})(\color{red}{8q}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(8q)}^2=4-64q^2\)
3. \((\color{blue}{8p^2}\color{red}{-4})(\color{blue}{8p^2}\color{red}{+4})=\color{blue}{(8p^2)}^2-\color{red}{(-4)}^2=64p^{4}-16\)
4. \((a+6)^2=a^2+\color{magenta}{2.a.6}+6^2=a^2\color{magenta}{+12a}+36\)
5. \((-14q^2-13)^2=(-14q^2)^2\color{magenta}{+2.(-14q^2).(-13)}+(-13)^2=196q^{4}\color{magenta}{+364q^2}+169\)
6. \((\color{red}{11s^2}\color{blue}{-10})(\color{red}{-11s^2}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(11s^2)}^2=100-121s^{4}\)
7. \((\color{blue}{14a}\color{red}{+3})(\color{blue}{14a}\color{red}{-3})=\color{blue}{(14a)}^2-\color{red}{(3)}^2=196a^2-9\)
8. \((11x-3)^2=(11x)^2+\color{magenta}{2.(11x).(-3)}+(-3)^2=121x^2\color{magenta}{-66x}+9\)
9. \((\color{blue}{a}\color{red}{-6})(\color{blue}{a}\color{red}{+6})=\color{blue}{a}^2-\color{red}{6}^2=a^2-36\)
10. \((b-1)^2=b^2+\color{magenta}{2.b.(-1)}+(-1)^2=b^2\color{magenta}{-2b}+1\)
11. \((\color{red}{-7x^5}\color{blue}{-12y})(\color{red}{7x^5}\color{blue}{-12y})=\color{blue}{(-12y)}^2-\color{red}{(7x^5)}^2=144y^2-49x^{10}\)
12. \((\color{blue}{a}\color{red}{-5})(\color{blue}{a}\color{red}{+5})=\color{blue}{a}^2-\color{red}{5}^2=a^2-25\)