Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((6a^3+16s)(6a^3+16s)=(6a^3+16s)^2=(6a^3)^2\color{magenta}{+2.(6a^3).(16s)}+(16s)^2=36a^{6}\color{magenta}{+192a^3s}+256s^2\)
2. \((\color{blue}{12q^4}\color{red}{-2})(\color{blue}{12q^4}\color{red}{+2})=\color{blue}{(12q^4)}^2-\color{red}{(-2)}^2=144q^{8}-4\)
3. \((\color{red}{4x^2}\color{blue}{+8})(\color{red}{-4x^2}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(4x^2)}^2=64-16x^{4}\)
4. \((q+9)(q+9)=(q+9)^2=q^2+\color{magenta}{2.q.9}+9^2=q^2\color{magenta}{+18q}+81\)
5. \((-16b^4-16)(-16b^4-16)=(-16b^4-16)^2=(-16b^4)^2\color{magenta}{+2.(-16b^4).(-16)}+(-16)^2=256b^{8}\color{magenta}{+512b^4}+256\)
6. \((\color{blue}{b}\color{red}{+15})(\color{blue}{b}\color{red}{-15})=\color{blue}{b}^2-\color{red}{15}^2=b^2-225\)
7. \((q-2)(q-2)=(q-2)^2=q^2+\color{magenta}{2.q.(-2)}+(-2)^2=q^2\color{magenta}{-4q}+4\)
8. \((-5s^2-10q)(-5s^2-10q)=(-5s^2-10q)^2=(-5s^2)^2\color{magenta}{+2.(-5s^2).(-10q)}+(-10q)^2=25s^{4}\color{magenta}{+100qs^2}+100q^2\)
9. \((q-11)^2=q^2+\color{magenta}{2.q.(-11)}+(-11)^2=q^2\color{magenta}{-22q}+121\)
10. \((\color{red}{-8p^4}\color{blue}{-6})(\color{red}{8p^4}\color{blue}{-6})=\color{blue}{(-6)}^2-\color{red}{(8p^4)}^2=36-64p^{8}\)
11. \((\color{red}{4x^3}\color{blue}{-9})(\color{red}{-4x^3}\color{blue}{-9})=\color{blue}{(-9)}^2-\color{red}{(4x^3)}^2=81-16x^{6}\)
12. \((\color{red}{6p^4}\color{blue}{-12})(\color{red}{-6p^4}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(6p^4)}^2=144-36p^{8}\)