Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-7b^4}\color{red}{+16})(\color{blue}{-7b^4}\color{red}{-16})=\color{blue}{(-7b^4)}^2-\color{red}{16}^2=49b^{8}-256\)
2. \((q^4-10a)(q^4-10a)=(q^4-10a)^2=(q^4)^2\color{magenta}{+2.(q^4).(-10a)}+(-10a)^2=q^{8}\color{magenta}{-20aq^4}+100a^2\)
3. \((6p-5)^2=(6p)^2+\color{magenta}{2.(6p).(-5)}+(-5)^2=36p^2\color{magenta}{-60p}+25\)
4. \((14a^3+14)^2=(14a^3)^2\color{magenta}{+2.(14a^3).14}+14^2=196a^{6}\color{magenta}{+392a^3}+196\)
5. \((\color{blue}{3x^5}\color{red}{-10})(\color{blue}{3x^5}\color{red}{+10})=\color{blue}{(3x^5)}^2-\color{red}{(-10)}^2=9x^{10}-100\)
6. \((15q^3+9)(15q^3+9)=(15q^3+9)^2=(15q^3)^2\color{magenta}{+2.(15q^3).9}+9^2=225q^{6}\color{magenta}{+270q^3}+81\)
7. \((11b^3+15s)(11b^3+15s)=(11b^3+15s)^2=(11b^3)^2\color{magenta}{+2.(11b^3).(15s)}+(15s)^2=121b^{6}\color{magenta}{+330b^3s}+225s^2\)
8. \((\color{red}{5b^5}\color{blue}{-11a})(\color{red}{-5b^5}\color{blue}{-11a})=\color{blue}{(-11a)}^2-\color{red}{(5b^5)}^2=121a^2-25b^{10}\)
9. \((14a^2+7)^2=(14a^2)^2\color{magenta}{+2.(14a^2).7}+7^2=196a^{4}\color{magenta}{+196a^2}+49\)
10. \((p-7)^2=p^2+\color{magenta}{2.p.(-7)}+(-7)^2=p^2\color{magenta}{-14p}+49\)
11. \((\color{red}{-9s^4}\color{blue}{+13})(\color{red}{9s^4}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(9s^4)}^2=169-81s^{8}\)
12. \((\color{blue}{q}\color{red}{-1})(\color{blue}{q}\color{red}{+1})=\color{blue}{q}^2-\color{red}{1}^2=q^2-1\)