Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{q}\color{red}{+7})(\color{blue}{q}\color{red}{-7})=\color{blue}{q}^2-\color{red}{7}^2=q^2-49\)
2. \((\color{red}{11b}\color{blue}{-4})(\color{red}{-11b}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(11b)}^2=16-121b^2\)
3. \((a-3)(a-3)=(a-3)^2=a^2+\color{magenta}{2.a.(-3)}+(-3)^2=a^2\color{magenta}{-6a}+9\)
4. \((-q^4+4)^2=(-q^4)^2\color{magenta}{+2.(-q^4).4}+4^2=1q^{8}\color{magenta}{-8q^4}+16\)
5. \((\color{red}{15b^3}\color{blue}{-7a})(\color{red}{-15b^3}\color{blue}{-7a})=\color{blue}{(-7a)}^2-\color{red}{(15b^3)}^2=49a^2-225b^{6}\)
6. \((-7x^2-4q)^2=(-7x^2)^2\color{magenta}{+2.(-7x^2).(-4q)}+(-4q)^2=49x^{4}\color{magenta}{+56qx^2}+16q^2\)
7. \((6p^5+9a)(6p^5+9a)=(6p^5+9a)^2=(6p^5)^2\color{magenta}{+2.(6p^5).(9a)}+(9a)^2=36p^{10}\color{magenta}{+108ap^5}+81a^2\)
8. \((-6s^5+4x)^2=(-6s^5)^2\color{magenta}{+2.(-6s^5).(4x)}+(4x)^2=36s^{10}\color{magenta}{-48s^5x}+16x^2\)
9. \((\color{blue}{3p^2}\color{red}{+4})(\color{blue}{3p^2}\color{red}{-4})=\color{blue}{(3p^2)}^2-\color{red}{4}^2=9p^{4}-16\)
10. \((\color{red}{5x^5}\color{blue}{+5})(\color{red}{-5x^5}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(5x^5)}^2=25-25x^{10}\)
11. \((-7x^5-14)^2=(-7x^5)^2\color{magenta}{+2.(-7x^5).(-14)}+(-14)^2=49x^{10}\color{magenta}{+196x^5}+196\)
12. \((3a^5+4)^2=(3a^5)^2\color{magenta}{+2.(3a^5).4}+4^2=9a^{10}\color{magenta}{+24a^5}+16\)