Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-7b-13)^2=(-7b)^2+\color{magenta}{2.(-7b).(-13)}+(-13)^2=49b^2\color{magenta}{+182b}+169\)
2. \((\color{red}{-9p}\color{blue}{-14})(\color{red}{9p}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(9p)}^2=196-81p^2\)
3. \((\color{blue}{b}\color{red}{-13})(\color{blue}{b}\color{red}{+13})=\color{blue}{b}^2-\color{red}{13}^2=b^2-169\)
4. \((\color{blue}{p}\color{red}{-8})(\color{blue}{p}\color{red}{+8})=\color{blue}{p}^2-\color{red}{8}^2=p^2-64\)
5. \((\color{red}{-6p^3}\color{blue}{+9})(\color{red}{6p^3}\color{blue}{+9})=\color{blue}{9}^2-\color{red}{(6p^3)}^2=81-36p^{6}\)
6. \((\color{blue}{5y^4}\color{red}{+5q})(\color{blue}{5y^4}\color{red}{-5q})=\color{blue}{(5y^4)}^2-\color{red}{(5q)}^2=25y^{8}-25q^2\)
7. \((\color{blue}{y}\color{red}{+4})(\color{blue}{y}\color{red}{-4})=\color{blue}{y}^2-\color{red}{4}^2=y^2-16\)
8. \((\color{red}{-5s^3}\color{blue}{-5a})(\color{red}{5s^3}\color{blue}{-5a})=\color{blue}{(-5a)}^2-\color{red}{(5s^3)}^2=25a^2-25s^{6}\)
9. \((12a^3+13s)(12a^3+13s)=(12a^3+13s)^2=(12a^3)^2\color{magenta}{+2.(12a^3).(13s)}+(13s)^2=144a^{6}\color{magenta}{+312a^3s}+169s^2\)
10. \((7s^2+9)(7s^2+9)=(7s^2+9)^2=(7s^2)^2\color{magenta}{+2.(7s^2).9}+9^2=49s^{4}\color{magenta}{+126s^2}+81\)
11. \((\color{blue}{-16b}\color{red}{+12})(\color{blue}{-16b}\color{red}{-12})=\color{blue}{(-16b)}^2-\color{red}{(12)}^2=256b^2-144\)
12. \((p+10)(p+10)=(p+10)^2=(p)^2+\color{magenta}{2.(p).10}+10^2=p^2\color{magenta}{+20p}+100\)