Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-2x^3-4)(-2x^3-4)=(-2x^3-4)^2=(-2x^3)^2\color{magenta}{+2.(-2x^3).(-4)}+(-4)^2=4x^{6}\color{magenta}{+16x^3}+16\)
2. \((9s^4-5)^2=(9s^4)^2\color{magenta}{+2.(9s^4).(-5)}+(-5)^2=81s^{8}\color{magenta}{-90s^4}+25\)
3. \((\color{blue}{-15p^3}\color{red}{-12q})(\color{blue}{-15p^3}\color{red}{+12q})=\color{blue}{(-15p^3)}^2-\color{red}{(-12q)}^2=225p^{6}-144q^2\)
4. \((-a^5-8)^2=(-a^5)^2\color{magenta}{+2.(-a^5).(-8)}+(-8)^2=1a^{10}\color{magenta}{+16a^5}+64\)
5. \((-a^5+11s)^2=(-a^5)^2\color{magenta}{+2.(-a^5).(11s)}+(11s)^2=a^{10}\color{magenta}{-22a^5s}+121s^2\)
6. \((-9y^4-10a)(-9y^4-10a)=(-9y^4-10a)^2=(-9y^4)^2\color{magenta}{+2.(-9y^4).(-10a)}+(-10a)^2=81y^{8}\color{magenta}{+180ay^4}+100a^2\)
7. \((\color{red}{5y}\color{blue}{-2})(\color{red}{-5y}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(5y)}^2=4-25y^2\)
8. \((a-13)(a-13)=(a-13)^2=(a)^2+\color{magenta}{2.(a).(-13)}+(-13)^2=a^2\color{magenta}{-26a}+169\)
9. \((a+3)^2=a^2+\color{magenta}{2.a.3}+3^2=a^2\color{magenta}{+6a}+9\)
10. \((-2p+11)(-2p+11)=(-2p+11)^2=(-2p)^2+\color{magenta}{2.(-2p).11}+11^2=4p^2\color{magenta}{-44p}+121\)
11. \((\color{blue}{-b^5}\color{red}{+14a})(\color{blue}{-b^5}\color{red}{-14a})=\color{blue}{(-b^5)}^2-\color{red}{(14a)}^2=b^{10}-196a^2\)
12. \((15y+14)(15y+14)=(15y+14)^2=(15y)^2+\color{magenta}{2.(15y).14}+14^2=225y^2\color{magenta}{+420y}+196\)