Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{a}\color{red}{-11})(\color{blue}{a}\color{red}{+11})=\color{blue}{a}^2-\color{red}{11}^2=a^2-121\)
2. \((\color{blue}{15a^4}\color{red}{+6q})(\color{blue}{15a^4}\color{red}{-6q})=\color{blue}{(15a^4)}^2-\color{red}{(6q)}^2=225a^{8}-36q^2\)
3. \((p+7)(p+7)=(p+7)^2=p^2+\color{magenta}{2.p.7}+7^2=p^2\color{magenta}{+14p}+49\)
4. \((-14y^4-16)^2=(-14y^4)^2\color{magenta}{+2.(-14y^4).(-16)}+(-16)^2=196y^{8}\color{magenta}{+448y^4}+256\)
5. \((y-2)^2=y^2+\color{magenta}{2.y.(-2)}+(-2)^2=y^2\color{magenta}{-4y}+4\)
6. \((b^3+8a)^2=(b^3)^2\color{magenta}{+2.(b^3).(8a)}+(8a)^2=b^{6}\color{magenta}{+16ab^3}+64a^2\)
7. \((-6x^2+10)^2=(-6x^2)^2\color{magenta}{+2.(-6x^2).10}+10^2=36x^{4}\color{magenta}{-120x^2}+100\)
8. \((-13y^3-7)^2=(-13y^3)^2\color{magenta}{+2.(-13y^3).(-7)}+(-7)^2=169y^{6}\color{magenta}{+182y^3}+49\)
9. \((4p^4-4)(4p^4-4)=(4p^4-4)^2=(4p^4)^2\color{magenta}{+2.(4p^4).(-4)}+(-4)^2=16p^{8}\color{magenta}{-32p^4}+16\)
10. \((-2b^5-9q)(-2b^5-9q)=(-2b^5-9q)^2=(-2b^5)^2\color{magenta}{+2.(-2b^5).(-9q)}+(-9q)^2=4b^{10}\color{magenta}{+36b^5q}+81q^2\)
11. \((\color{red}{16y}\color{blue}{-8})(\color{red}{-16y}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(16y)}^2=64-256y^2\)
12. \((\color{red}{-7b}\color{blue}{+1})(\color{red}{7b}\color{blue}{+1})=\color{blue}{1}^2-\color{red}{(7b)}^2=1-49b^2\)