Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-3x^2}\color{blue}{-11s})(\color{red}{3x^2}\color{blue}{-11s})=\color{blue}{(-11s)}^2-\color{red}{(3x^2)}^2=121s^2-9x^{4}\)
2. \((-2q^4-6x)(-2q^4-6x)=(-2q^4-6x)^2=(-2q^4)^2\color{magenta}{+2.(-2q^4).(-6x)}+(-6x)^2=4q^{8}\color{magenta}{+24q^4x}+36x^2\)
3. \((-7y^4-7)^2=(-7y^4)^2\color{magenta}{+2.(-7y^4).(-7)}+(-7)^2=49y^{8}\color{magenta}{+98y^4}+49\)
4. \((\color{blue}{b}\color{red}{+10})(\color{blue}{b}\color{red}{-10})=\color{blue}{b}^2-\color{red}{10}^2=b^2-100\)
5. \((\color{red}{2x^2}\color{blue}{+13})(\color{red}{-2x^2}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(2x^2)}^2=169-4x^{4}\)
6. \((16q-11)(16q-11)=(16q-11)^2=(16q)^2+\color{magenta}{2.(16q).(-11)}+(-11)^2=256q^2\color{magenta}{-352q}+121\)
7. \((-9a^5-12s)(-9a^5-12s)=(-9a^5-12s)^2=(-9a^5)^2\color{magenta}{+2.(-9a^5).(-12s)}+(-12s)^2=81a^{10}\color{magenta}{+216a^5s}+144s^2\)
8. \((b-11)(b-11)=(b-11)^2=b^2+\color{magenta}{2.b.(-11)}+(-11)^2=b^2\color{magenta}{-22b}+121\)
9. \((\color{blue}{s}\color{red}{+4})(\color{blue}{s}\color{red}{-4})=\color{blue}{s}^2-\color{red}{4}^2=s^2-16\)
10. \((\color{red}{12a^3}\color{blue}{-7})(\color{red}{-12a^3}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(12a^3)}^2=49-144a^{6}\)
11. \((-3q^3-14p)(-3q^3-14p)=(-3q^3-14p)^2=(-3q^3)^2\color{magenta}{+2.(-3q^3).(-14p)}+(-14p)^2=9q^{6}\color{magenta}{+84pq^3}+196p^2\)
12. \((9p^5+16s)(9p^5+16s)=(9p^5+16s)^2=(9p^5)^2\color{magenta}{+2.(9p^5).(16s)}+(16s)^2=81p^{10}\color{magenta}{+288p^5s}+256s^2\)