Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((10q^4-15x)(10q^4-15x)=(10q^4-15x)^2=(10q^4)^2\color{magenta}{+2.(10q^4).(-15x)}+(-15x)^2=100q^{8}\color{magenta}{-300q^4x}+225x^2\)
2. \((\color{red}{7a^5}\color{blue}{+2})(\color{red}{-7a^5}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(7a^5)}^2=4-49a^{10}\)
3. \((\color{red}{10a^3}\color{blue}{-9y})(\color{red}{-10a^3}\color{blue}{-9y})=\color{blue}{(-9y)}^2-\color{red}{(10a^3)}^2=81y^2-100a^{6}\)
4. \((-8y^5+9a)^2=(-8y^5)^2\color{magenta}{+2.(-8y^5).(9a)}+(9a)^2=64y^{10}\color{magenta}{-144ay^5}+81a^2\)
5. \((\color{blue}{-13b^2}\color{red}{+11p})(\color{blue}{-13b^2}\color{red}{-11p})=\color{blue}{(-13b^2)}^2-\color{red}{(11p)}^2=169b^{4}-121p^2\)
6. \((2s^3-6)^2=(2s^3)^2\color{magenta}{+2.(2s^3).(-6)}+(-6)^2=4s^{6}\color{magenta}{-24s^3}+36\)
7. \((15q^4+8x)(15q^4+8x)=(15q^4+8x)^2=(15q^4)^2\color{magenta}{+2.(15q^4).(8x)}+(8x)^2=225q^{8}\color{magenta}{+240q^4x}+64x^2\)
8. \((s+14)^2=s^2+\color{magenta}{2.s.14}+14^2=s^2\color{magenta}{+28s}+196\)
9. \((-13a^2+b)(-13a^2+b)=(-13a^2+b)^2=(-13a^2)^2\color{magenta}{+2.(-13a^2).(b)}+(b)^2=169a^{4}\color{magenta}{-26a^2b}+1b^2\)
10. \((-y^5+9a)^2=(-y^5)^2\color{magenta}{+2.(-y^5).(9a)}+(9a)^2=y^{10}\color{magenta}{-18ay^5}+81a^2\)
11. \((-10s^4-6b)^2=(-10s^4)^2\color{magenta}{+2.(-10s^4).(-6b)}+(-6b)^2=100s^{8}\color{magenta}{+120bs^4}+36b^2\)
12. \((-12s+8)(-12s+8)=(-12s+8)^2=(-12s)^2+\color{magenta}{2.(-12s).8}+8^2=144s^2\color{magenta}{-192s}+64\)