Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{x}\color{red}{-12})(\color{blue}{x}\color{red}{+12})=\color{blue}{x}^2-\color{red}{12}^2=x^2-144\)
2. \((-10a^3+14)^2=(-10a^3)^2\color{magenta}{+2.(-10a^3).14}+14^2=100a^{6}\color{magenta}{-280a^3}+196\)
3. \((\color{red}{-11b^3}\color{blue}{-9x})(\color{red}{11b^3}\color{blue}{-9x})=\color{blue}{(-9x)}^2-\color{red}{(11b^3)}^2=81x^2-121b^{6}\)
4. \((-7s^5+15)(-7s^5+15)=(-7s^5+15)^2=(-7s^5)^2\color{magenta}{+2.(-7s^5).15}+15^2=49s^{10}\color{magenta}{-210s^5}+225\)
5. \((a-5)^2=a^2+\color{magenta}{2.a.(-5)}+(-5)^2=a^2\color{magenta}{-10a}+25\)
6. \((\color{blue}{-11s^2}\color{red}{-12b})(\color{blue}{-11s^2}\color{red}{+12b})=\color{blue}{(-11s^2)}^2-\color{red}{(-12b)}^2=121s^{4}-144b^2\)
7. \((\color{red}{9b^3}\color{blue}{-10})(\color{red}{-9b^3}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(9b^3)}^2=100-81b^{6}\)
8. \((\color{red}{-2y}\color{blue}{-4})(\color{red}{2y}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(2y)}^2=16-4y^2\)
9. \((11p+4)^2=(11p)^2+\color{magenta}{2.(11p).4}+4^2=121p^2\color{magenta}{+88p}+16\)
10. \((15x^2-14y)(15x^2-14y)=(15x^2-14y)^2=(15x^2)^2\color{magenta}{+2.(15x^2).(-14y)}+(-14y)^2=225x^{4}\color{magenta}{-420x^2y}+196y^2\)
11. \((\color{red}{-14b^5}\color{blue}{-3})(\color{red}{14b^5}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(14b^5)}^2=9-196b^{10}\)
12. \((15a^3+14y)(15a^3+14y)=(15a^3+14y)^2=(15a^3)^2\color{magenta}{+2.(15a^3).(14y)}+(14y)^2=225a^{6}\color{magenta}{+420a^3y}+196y^2\)