Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((p-13)(p-13)\)
2. \((s+12)^2\)
3. \((-16p^5+3a)(-16p^5-3a)\)
4. \((8b^2+4y)(8b^2-4y)\)
5. \((-7a^5+5)(7a^5+5)\)
6. \((-12y+9)(12y+9)\)
7. \((p+6)(p-6)\)
8. \((3s^5-15)(-3s^5-15)\)
9. \((14q^5-1)^2\)
10. \((-3s+7)^2\)
11. \((15a^2-4)^2\)
12. \((12y^2-11b)^2\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p-13)(p-13)=(p-13)^2=p^2+\color{magenta}{2.p.(-13)}+(-13)^2=p^2\color{magenta}{-26p}+169\)
2. \((s+12)^2=s^2+\color{magenta}{2.s.12}+12^2=s^2\color{magenta}{+24s}+144\)
3. \((\color{blue}{-16p^5}\color{red}{+3a})(\color{blue}{-16p^5}\color{red}{-3a})=\color{blue}{(-16p^5)}^2-\color{red}{(3a)}^2=256p^{10}-9a^2\)
4. \((\color{blue}{8b^2}\color{red}{+4y})(\color{blue}{8b^2}\color{red}{-4y})=\color{blue}{(8b^2)}^2-\color{red}{(4y)}^2=64b^{4}-16y^2\)
5. \((\color{red}{-7a^5}\color{blue}{+5})(\color{red}{7a^5}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(7a^5)}^2=25-49a^{10}\)
6. \((\color{red}{-12y}\color{blue}{+9})(\color{red}{12y}\color{blue}{+9})=\color{blue}{9}^2-\color{red}{(12y)}^2=81-144y^2\)
7. \((\color{blue}{p}\color{red}{+6})(\color{blue}{p}\color{red}{-6})=\color{blue}{p}^2-\color{red}{6}^2=p^2-36\)
8. \((\color{red}{3s^5}\color{blue}{-15})(\color{red}{-3s^5}\color{blue}{-15})=\color{blue}{(-15)}^2-\color{red}{(3s^5)}^2=225-9s^{10}\)
9. \((14q^5-1)^2=(14q^5)^2\color{magenta}{+2.(14q^5).(-1)}+(-1)^2=196q^{10}\color{magenta}{-28q^5}+1\)
10. \((-3s+7)^2=(-3s)^2+\color{magenta}{2.(-3s).7}+7^2=9s^2\color{magenta}{-42s}+49\)
11. \((15a^2-4)^2=(15a^2)^2\color{magenta}{+2.(15a^2).(-4)}+(-4)^2=225a^{4}\color{magenta}{-120a^2}+16\)
12. \((12y^2-11b)^2=(12y^2)^2\color{magenta}{+2.(12y^2).(-11b)}+(-11b)^2=144y^{4}\color{magenta}{-264by^2}+121b^2\)