Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((13p^4-1)^2=(13p^4)^2\color{magenta}{+2.(13p^4).(-1)}+(-1)^2=169p^{8}\color{magenta}{-26p^4}+1\)
2. \((\color{blue}{4p^5}\color{red}{-16b})(\color{blue}{4p^5}\color{red}{+16b})=\color{blue}{(4p^5)}^2-\color{red}{(-16b)}^2=16p^{10}-256b^2\)
3. \((s-9)^2=s^2+\color{magenta}{2.s.(-9)}+(-9)^2=s^2\color{magenta}{-18s}+81\)
4. \((-7q^5-2)^2=(-7q^5)^2\color{magenta}{+2.(-7q^5).(-2)}+(-2)^2=49q^{10}\color{magenta}{+28q^5}+4\)
5. \((-11s^5-9q)^2=(-11s^5)^2\color{magenta}{+2.(-11s^5).(-9q)}+(-9q)^2=121s^{10}\color{magenta}{+198qs^5}+81q^2\)
6. \((13b-8)(13b-8)=(13b-8)^2=(13b)^2+\color{magenta}{2.(13b).(-8)}+(-8)^2=169b^2\color{magenta}{-208b}+64\)
7. \((\color{blue}{15p^5}\color{red}{-12b})(\color{blue}{15p^5}\color{red}{+12b})=\color{blue}{(15p^5)}^2-\color{red}{(-12b)}^2=225p^{10}-144b^2\)
8. \((\color{blue}{-16q^4}\color{red}{-3y})(\color{blue}{-16q^4}\color{red}{+3y})=\color{blue}{(-16q^4)}^2-\color{red}{(-3y)}^2=256q^{8}-9y^2\)
9. \((\color{blue}{15s}\color{red}{+1})(\color{blue}{15s}\color{red}{-1})=\color{blue}{(15s)}^2-\color{red}{(1)}^2=225s^2-1\)
10. \((10b^4-13)^2=(10b^4)^2\color{magenta}{+2.(10b^4).(-13)}+(-13)^2=100b^{8}\color{magenta}{-260b^4}+169\)
11. \((\color{blue}{-5s^5}\color{red}{+11})(\color{blue}{-5s^5}\color{red}{-11})=\color{blue}{(-5s^5)}^2-\color{red}{11}^2=25s^{10}-121\)
12. \((16s^3-4x)(16s^3-4x)=(16s^3-4x)^2=(16s^3)^2\color{magenta}{+2.(16s^3).(-4x)}+(-4x)^2=256s^{6}\color{magenta}{-128s^3x}+16x^2\)