Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p-8)^2=p^2+\color{magenta}{2.p.(-8)}+(-8)^2=p^2\color{magenta}{-16p}+64\)
2. \((-8q-16)(-8q-16)=(-8q-16)^2=(-8q)^2+\color{magenta}{2.(-8q).(-16)}+(-16)^2=64q^2\color{magenta}{+256q}+256\)
3. \((\color{blue}{-11y}\color{red}{+1})(\color{blue}{-11y}\color{red}{-1})=\color{blue}{(-11y)}^2-\color{red}{(1)}^2=121y^2-1\)
4. \((a-12)^2=a^2+\color{magenta}{2.a.(-12)}+(-12)^2=a^2\color{magenta}{-24a}+144\)
5. \((-4y-6)^2=(-4y)^2+\color{magenta}{2.(-4y).(-6)}+(-6)^2=16y^2\color{magenta}{+48y}+36\)
6. \((\color{blue}{14a^3}\color{red}{-4})(\color{blue}{14a^3}\color{red}{+4})=\color{blue}{(14a^3)}^2-\color{red}{(-4)}^2=196a^{6}-16\)
7. \((\color{blue}{a}\color{red}{-3})(\color{blue}{a}\color{red}{+3})=\color{blue}{a}^2-\color{red}{3}^2=a^2-9\)
8. \((13q+9)(13q+9)=(13q+9)^2=(13q)^2+\color{magenta}{2.(13q).9}+9^2=169q^2\color{magenta}{+234q}+81\)
9. \((\color{blue}{12p^3}\color{red}{-6s})(\color{blue}{12p^3}\color{red}{+6s})=\color{blue}{(12p^3)}^2-\color{red}{(-6s)}^2=144p^{6}-36s^2\)
10. \((\color{red}{-9y}\color{blue}{-8})(\color{red}{9y}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(9y)}^2=64-81y^2\)
11. \((b+15)(b+15)=(b+15)^2=b^2+\color{magenta}{2.b.15}+15^2=b^2\color{magenta}{+30b}+225\)
12. \((6s+11)^2=(6s)^2+\color{magenta}{2.(6s).11}+11^2=36s^2\color{magenta}{+132s}+121\)