Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((5a^2+15)(5a^2+15)=(5a^2+15)^2=(5a^2)^2\color{magenta}{+2.(5a^2).15}+15^2=25a^{4}\color{magenta}{+150a^2}+225\)
2. \((\color{blue}{3q^2}\color{red}{+13y})(\color{blue}{3q^2}\color{red}{-13y})=\color{blue}{(3q^2)}^2-\color{red}{(13y)}^2=9q^{4}-169y^2\)
3. \((-15y^3+11x)^2=(-15y^3)^2\color{magenta}{+2.(-15y^3).(11x)}+(11x)^2=225y^{6}\color{magenta}{-330xy^3}+121x^2\)
4. \((\color{blue}{p}\color{red}{+13})(\color{blue}{p}\color{red}{-13})=\color{blue}{p}^2-\color{red}{13}^2=p^2-169\)
5. \((\color{blue}{-15q}\color{red}{-15})(\color{blue}{-15q}\color{red}{+15})=\color{blue}{(-15q)}^2-\color{red}{(-15)}^2=225q^2-225\)
6. \((s+12)^2=s^2+\color{magenta}{2.s.12}+12^2=s^2\color{magenta}{+24s}+144\)
7. \((\color{red}{6s^3}\color{blue}{-7a})(\color{red}{-6s^3}\color{blue}{-7a})=\color{blue}{(-7a)}^2-\color{red}{(6s^3)}^2=49a^2-36s^{6}\)
8. \((\color{blue}{-4q}\color{red}{-10})(\color{blue}{-4q}\color{red}{+10})=\color{blue}{(-4q)}^2-\color{red}{(-10)}^2=16q^2-100\)
9. \((\color{red}{12b}\color{blue}{-13})(\color{red}{-12b}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(12b)}^2=169-144b^2\)
10. \((b-5)(b-5)=(b-5)^2=b^2+\color{magenta}{2.b.(-5)}+(-5)^2=b^2\color{magenta}{-10b}+25\)
11. \((-7p+1)^2=(-7p)^2+\color{magenta}{2.(-7p).1}+1^2=49p^2\color{magenta}{-14p}+1\)
12. \((\color{blue}{-x^2}\color{red}{+3q})(\color{blue}{-x^2}\color{red}{-3q})=\color{blue}{(-x^2)}^2-\color{red}{(3q)}^2=x^{4}-9q^2\)