Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-16p^5}\color{blue}{-14})(\color{red}{16p^5}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(16p^5)}^2=196-256p^{10}\)
2. \((\color{blue}{y}\color{red}{-11})(\color{blue}{y}\color{red}{+11})=\color{blue}{y}^2-\color{red}{11}^2=y^2-121\)
3. \((-12x^5-12)(-12x^5-12)=(-12x^5-12)^2=(-12x^5)^2\color{magenta}{+2.(-12x^5).(-12)}+(-12)^2=144x^{10}\color{magenta}{+288x^5}+144\)
4. \((\color{red}{-3p}\color{blue}{+11})(\color{red}{3p}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(3p)}^2=121-9p^2\)
5. \((-4p^5+10)(-4p^5+10)=(-4p^5+10)^2=(-4p^5)^2\color{magenta}{+2.(-4p^5).10}+10^2=16p^{10}\color{magenta}{-80p^5}+100\)
6. \((-9x-9)^2=(-9x)^2+\color{magenta}{2.(-9x).(-9)}+(-9)^2=81x^2\color{magenta}{+162x}+81\)
7. \((\color{blue}{13y^3}\color{red}{-15p})(\color{blue}{13y^3}\color{red}{+15p})=\color{blue}{(13y^3)}^2-\color{red}{(-15p)}^2=169y^{6}-225p^2\)
8. \((9y^4+16x)(9y^4+16x)=(9y^4+16x)^2=(9y^4)^2\color{magenta}{+2.(9y^4).(16x)}+(16x)^2=81y^{8}\color{magenta}{+288xy^4}+256x^2\)
9. \((y+6)^2=y^2+\color{magenta}{2.y.6}+6^2=y^2\color{magenta}{+12y}+36\)
10. \((2p^3+14)^2=(2p^3)^2\color{magenta}{+2.(2p^3).14}+14^2=4p^{6}\color{magenta}{+56p^3}+196\)
11. \((-7q+3)^2=(-7q)^2+\color{magenta}{2.(-7q).3}+3^2=49q^2\color{magenta}{-42q}+9\)
12. \((\color{red}{-6a^5}\color{blue}{+16})(\color{red}{6a^5}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(6a^5)}^2=256-36a^{10}\)