Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((6a+12)^2=(6a)^2+\color{magenta}{2.(6a).12}+12^2=36a^2\color{magenta}{+144a}+144\)
2. \((-b^5-5a)^2=(-b^5)^2\color{magenta}{+2.(-b^5).(-5a)}+(-5a)^2=b^{10}\color{magenta}{+10ab^5}+25a^2\)
3. \((p-15)(p-15)=(p-15)^2=p^2+\color{magenta}{2.p.(-15)}+(-15)^2=p^2\color{magenta}{-30p}+225\)
4. \((p+10)(p+10)=(p+10)^2=p^2+\color{magenta}{2.p.10}+10^2=p^2\color{magenta}{+20p}+100\)
5. \((5x^2+7b)(5x^2+7b)=(5x^2+7b)^2=(5x^2)^2\color{magenta}{+2.(5x^2).(7b)}+(7b)^2=25x^{4}\color{magenta}{+70bx^2}+49b^2\)
6. \((8a+14)^2=(8a)^2+\color{magenta}{2.(8a).14}+14^2=64a^2\color{magenta}{+224a}+196\)
7. \((\color{red}{-12b}\color{blue}{-1})(\color{red}{12b}\color{blue}{-1})=\color{blue}{(-1)}^2-\color{red}{(12b)}^2=1-144b^2\)
8. \((\color{red}{-12s^3}\color{blue}{-7})(\color{red}{12s^3}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(12s^3)}^2=49-144s^{6}\)
9. \((\color{blue}{b}\color{red}{-4})(\color{blue}{b}\color{red}{+4})=\color{blue}{b}^2-\color{red}{4}^2=b^2-16\)
10. \((q-13)^2=q^2+\color{magenta}{2.q.(-13)}+(-13)^2=q^2\color{magenta}{-26q}+169\)
11. \((\color{red}{-14s}\color{blue}{+14})(\color{red}{14s}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(14s)}^2=196-196s^2\)
12. \((p-6)^2=p^2+\color{magenta}{2.p.(-6)}+(-6)^2=p^2\color{magenta}{-12p}+36\)