Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-6q}\color{blue}{-12})(\color{red}{6q}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(6q)}^2=144-36q^2\)
2. \((\color{blue}{16p}\color{red}{-3})(\color{blue}{16p}\color{red}{+3})=\color{blue}{(16p)}^2-\color{red}{(-3)}^2=256p^2-9\)
3. \((q-2)(q-2)=(q-2)^2=q^2+\color{magenta}{2.q.(-2)}+(-2)^2=q^2\color{magenta}{-4q}+4\)
4. \((-6y^2-7)(-6y^2-7)=(-6y^2-7)^2=(-6y^2)^2\color{magenta}{+2.(-6y^2).(-7)}+(-7)^2=36y^{4}\color{magenta}{+84y^2}+49\)
5. \((-6a^4+3s)(-6a^4+3s)=(-6a^4+3s)^2=(-6a^4)^2\color{magenta}{+2.(-6a^4).(3s)}+(3s)^2=36a^{8}\color{magenta}{-36a^4s}+9s^2\)
6. \((-11y^5-5)(-11y^5-5)=(-11y^5-5)^2=(-11y^5)^2\color{magenta}{+2.(-11y^5).(-5)}+(-5)^2=121y^{10}\color{magenta}{+110y^5}+25\)
7. \((x+5)^2=x^2+\color{magenta}{2.x.5}+5^2=x^2\color{magenta}{+10x}+25\)
8. \((q-10)(q-10)=(q-10)^2=q^2+\color{magenta}{2.q.(-10)}+(-10)^2=q^2\color{magenta}{-20q}+100\)
9. \((2x^4+15)^2=(2x^4)^2\color{magenta}{+2.(2x^4).15}+15^2=4x^{8}\color{magenta}{+60x^4}+225\)
10. \((2s^2+3)^2=(2s^2)^2\color{magenta}{+2.(2s^2).3}+3^2=4s^{4}\color{magenta}{+12s^2}+9\)
11. \((\color{blue}{-6q^4}\color{red}{-10})(\color{blue}{-6q^4}\color{red}{+10})=\color{blue}{(-6q^4)}^2-\color{red}{(-10)}^2=36q^{8}-100\)
12. \((\color{red}{6p^5}\color{blue}{-4b})(\color{red}{-6p^5}\color{blue}{-4b})=\color{blue}{(-4b)}^2-\color{red}{(6p^5)}^2=16b^2-36p^{10}\)