Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p-6)^2=p^2+\color{magenta}{2.p.(-6)}+(-6)^2=p^2\color{magenta}{-12p}+36\)
2. \((-9y^5+9)^2=(-9y^5)^2\color{magenta}{+2.(-9y^5).9}+9^2=81y^{10}\color{magenta}{-162y^5}+81\)
3. \((\color{blue}{s}\color{red}{-14})(\color{blue}{s}\color{red}{+14})=\color{blue}{s}^2-\color{red}{14}^2=s^2-196\)
4. \((\color{blue}{b}\color{red}{+3})(\color{blue}{b}\color{red}{-3})=\color{blue}{b}^2-\color{red}{3}^2=b^2-9\)
5. \((\color{blue}{b}\color{red}{+11})(\color{blue}{b}\color{red}{-11})=\color{blue}{b}^2-\color{red}{11}^2=b^2-121\)
6. \((b-2)^2=b^2+\color{magenta}{2.b.(-2)}+(-2)^2=b^2\color{magenta}{-4b}+4\)
7. \((-16y-3)^2=(-16y)^2+\color{magenta}{2.(-16y).(-3)}+(-3)^2=256y^2\color{magenta}{+96y}+9\)
8. \((\color{blue}{-b}\color{red}{+8})(\color{blue}{-b}\color{red}{-8})=\color{blue}{(-b)}^2-\color{red}{(8)}^2=b^2-64\)
9. \((-2y+4)(-2y+4)=(-2y+4)^2=(-2y)^2+\color{magenta}{2.(-2y).4}+4^2=4y^2\color{magenta}{-16y}+16\)
10. \((\color{blue}{-7b^5}\color{red}{+4a})(\color{blue}{-7b^5}\color{red}{-4a})=\color{blue}{(-7b^5)}^2-\color{red}{(4a)}^2=49b^{10}-16a^2\)
11. \((-15p-7)(-15p-7)=(-15p-7)^2=(-15p)^2+\color{magenta}{2.(-15p).(-7)}+(-7)^2=225p^2\color{magenta}{+210p}+49\)
12. \((-5p^4+13y)^2=(-5p^4)^2\color{magenta}{+2.(-5p^4).(13y)}+(13y)^2=25p^{8}\color{magenta}{-130p^4y}+169y^2\)