Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-10s^4}\color{red}{+10})(\color{blue}{-10s^4}\color{red}{-10})=\color{blue}{(-10s^4)}^2-\color{red}{10}^2=100s^{8}-100\)
2. \((3x^4+12)(3x^4+12)=(3x^4+12)^2=(3x^4)^2\color{magenta}{+2.(3x^4).12}+12^2=9x^{8}\color{magenta}{+72x^4}+144\)
3. \((\color{red}{16b}\color{blue}{+3})(\color{red}{-16b}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(16b)}^2=9-256b^2\)
4. \((\color{blue}{-4p}\color{red}{-10})(\color{blue}{-4p}\color{red}{+10})=\color{blue}{(-4p)}^2-\color{red}{(-10)}^2=16p^2-100\)
5. \((6y^2+10p)^2=(6y^2)^2\color{magenta}{+2.(6y^2).(10p)}+(10p)^2=36y^{4}\color{magenta}{+120py^2}+100p^2\)
6. \((\color{blue}{4s^4}\color{red}{+11x})(\color{blue}{4s^4}\color{red}{-11x})=\color{blue}{(4s^4)}^2-\color{red}{(11x)}^2=16s^{8}-121x^2\)
7. \((a-4)(a-4)=(a-4)^2=a^2+\color{magenta}{2.a.(-4)}+(-4)^2=a^2\color{magenta}{-8a}+16\)
8. \((\color{red}{8a^4}\color{blue}{+6q})(\color{red}{-8a^4}\color{blue}{+6q})=\color{blue}{(6q)}^2-\color{red}{(8a^4)}^2=36q^2-64a^{8}\)
9. \((14a^3-12q)^2=(14a^3)^2\color{magenta}{+2.(14a^3).(-12q)}+(-12q)^2=196a^{6}\color{magenta}{-336a^3q}+144q^2\)
10. \((-3a-16)^2=(-3a)^2+\color{magenta}{2.(-3a).(-16)}+(-16)^2=9a^2\color{magenta}{+96a}+256\)
11. \((-15q-6)(-15q-6)=(-15q-6)^2=(-15q)^2+\color{magenta}{2.(-15q).(-6)}+(-6)^2=225q^2\color{magenta}{+180q}+36\)
12. \((-11p^4-2)^2=(-11p^4)^2\color{magenta}{+2.(-11p^4).(-2)}+(-2)^2=121p^{8}\color{magenta}{+44p^4}+4\)