Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15y^3-16q)(15y^3-16q)=(15y^3-16q)^2=(15y^3)^2\color{magenta}{+2.(15y^3).(-16q)}+(-16q)^2=225y^{6}\color{magenta}{-480qy^3}+256q^2\)
2. \((-9s^3+14a)(-9s^3+14a)=(-9s^3+14a)^2=(-9s^3)^2\color{magenta}{+2.(-9s^3).(14a)}+(14a)^2=81s^{6}\color{magenta}{-252as^3}+196a^2\)
3. \((\color{red}{-14x^3}\color{blue}{+11})(\color{red}{14x^3}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(14x^3)}^2=121-196x^{6}\)
4. \((-11p^3+15)(-11p^3+15)=(-11p^3+15)^2=(-11p^3)^2\color{magenta}{+2.(-11p^3).15}+15^2=121p^{6}\color{magenta}{-330p^3}+225\)
5. \((6b+2)(6b+2)=(6b+2)^2=(6b)^2+\color{magenta}{2.(6b).2}+2^2=36b^2\color{magenta}{+24b}+4\)
6. \((-13p^4+6y)(-13p^4+6y)=(-13p^4+6y)^2=(-13p^4)^2\color{magenta}{+2.(-13p^4).(6y)}+(6y)^2=169p^{8}\color{magenta}{-156p^4y}+36y^2\)
7. \((\color{blue}{-5p^3}\color{red}{-7})(\color{blue}{-5p^3}\color{red}{+7})=\color{blue}{(-5p^3)}^2-\color{red}{(-7)}^2=25p^{6}-49\)
8. \((\color{blue}{-11s^3}\color{red}{-2a})(\color{blue}{-11s^3}\color{red}{+2a})=\color{blue}{(-11s^3)}^2-\color{red}{(-2a)}^2=121s^{6}-4a^2\)
9. \((y+5)^2=y^2+\color{magenta}{2.y.5}+5^2=y^2\color{magenta}{+10y}+25\)
10. \((10x^5+11b)(10x^5+11b)=(10x^5+11b)^2=(10x^5)^2\color{magenta}{+2.(10x^5).(11b)}+(11b)^2=100x^{10}\color{magenta}{+220bx^5}+121b^2\)
11. \((10q^5-13)(10q^5-13)=(10q^5-13)^2=(10q^5)^2\color{magenta}{+2.(10q^5).(-13)}+(-13)^2=100q^{10}\color{magenta}{-260q^5}+169\)
12. \((y^2+13a)^2=(y^2)^2\color{magenta}{+2.(y^2).(13a)}+(13a)^2=y^{4}\color{magenta}{+26ay^2}+169a^2\)