Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((4q+1)(4q+1)=(4q+1)^2=(4q)^2+\color{magenta}{2.(4q).1}+1^2=16q^2\color{magenta}{+8q}+1\)
2. \((-16x+13)(-16x+13)=(-16x+13)^2=(-16x)^2+\color{magenta}{2.(-16x).13}+13^2=256x^2\color{magenta}{-416x}+169\)
3. \((-12p^5+6)^2=(-12p^5)^2\color{magenta}{+2.(-12p^5).6}+6^2=144p^{10}\color{magenta}{-144p^5}+36\)
4. \((\color{red}{11a^2}\color{blue}{-11b})(\color{red}{-11a^2}\color{blue}{-11b})=\color{blue}{(-11b)}^2-\color{red}{(11a^2)}^2=121b^2-121a^{4}\)
5. \((\color{red}{-6a^2}\color{blue}{+3})(\color{red}{6a^2}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(6a^2)}^2=9-36a^{4}\)
6. \((\color{blue}{a}\color{red}{-2})(\color{blue}{a}\color{red}{+2})=\color{blue}{a}^2-\color{red}{2}^2=a^2-4\)
7. \((-14q^3+1)^2=(-14q^3)^2\color{magenta}{+2.(-14q^3).1}+1^2=196q^{6}\color{magenta}{-28q^3}+1\)
8. \((\color{blue}{13x^3}\color{red}{+2})(\color{blue}{13x^3}\color{red}{-2})=\color{blue}{(13x^3)}^2-\color{red}{2}^2=169x^{6}-4\)
9. \((2q^4-4)^2=(2q^4)^2\color{magenta}{+2.(2q^4).(-4)}+(-4)^2=4q^{8}\color{magenta}{-16q^4}+16\)
10. \((y-14)(y-14)=(y-14)^2=y^2+\color{magenta}{2.y.(-14)}+(-14)^2=y^2\color{magenta}{-28y}+196\)
11. \((12s^5-12)^2=(12s^5)^2\color{magenta}{+2.(12s^5).(-12)}+(-12)^2=144s^{10}\color{magenta}{-288s^5}+144\)
12. \((3q^3+2a)^2=(3q^3)^2\color{magenta}{+2.(3q^3).(2a)}+(2a)^2=9q^{6}\color{magenta}{+12aq^3}+4a^2\)