Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{12q^5}\color{red}{+13})(\color{blue}{12q^5}\color{red}{-13})=\color{blue}{(12q^5)}^2-\color{red}{13}^2=144q^{10}-169\)
2. \((\color{blue}{y}\color{red}{+13})(\color{blue}{y}\color{red}{-13})=\color{blue}{y}^2-\color{red}{13}^2=y^2-169\)
3. \((\color{blue}{9y}\color{red}{+12})(\color{blue}{9y}\color{red}{-12})=\color{blue}{(9y)}^2-\color{red}{(12)}^2=81y^2-144\)
4. \((-11b^2-11y)^2=(-11b^2)^2\color{magenta}{+2.(-11b^2).(-11y)}+(-11y)^2=121b^{4}\color{magenta}{+242b^2y}+121y^2\)
5. \((\color{blue}{s}\color{red}{+9})(\color{blue}{s}\color{red}{-9})=\color{blue}{s}^2-\color{red}{9}^2=s^2-81\)
6. \((\color{red}{-5b^2}\color{blue}{-14y})(\color{red}{5b^2}\color{blue}{-14y})=\color{blue}{(-14y)}^2-\color{red}{(5b^2)}^2=196y^2-25b^{4}\)
7. \((-15b-15)(-15b-15)=(-15b-15)^2=(-15b)^2+\color{magenta}{2.(-15b).(-15)}+(-15)^2=225b^2\color{magenta}{+450b}+225\)
8. \((2x+1)(2x+1)=(2x+1)^2=(2x)^2+\color{magenta}{2.(2x).1}+1^2=4x^2\color{magenta}{+4x}+1\)
9. \((\color{blue}{-3a^5}\color{red}{-16})(\color{blue}{-3a^5}\color{red}{+16})=\color{blue}{(-3a^5)}^2-\color{red}{(-16)}^2=9a^{10}-256\)
10. \((\color{blue}{-14s^5}\color{red}{+8})(\color{blue}{-14s^5}\color{red}{-8})=\color{blue}{(-14s^5)}^2-\color{red}{8}^2=196s^{10}-64\)
11. \((15p^4-7s)^2=(15p^4)^2\color{magenta}{+2.(15p^4).(-7s)}+(-7s)^2=225p^{8}\color{magenta}{-210p^4s}+49s^2\)
12. \((x-14)(x-14)=(x-14)^2=x^2+\color{magenta}{2.x.(-14)}+(-14)^2=x^2\color{magenta}{-28x}+196\)