Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a-2)^2=a^2+\color{magenta}{2.a.(-2)}+(-2)^2=a^2\color{magenta}{-4a}+4\)
2. \((\color{blue}{-4a^4}\color{red}{-10p})(\color{blue}{-4a^4}\color{red}{+10p})=\color{blue}{(-4a^4)}^2-\color{red}{(-10p)}^2=16a^{8}-100p^2\)
3. \((15x^2-15)(15x^2-15)=(15x^2-15)^2=(15x^2)^2\color{magenta}{+2.(15x^2).(-15)}+(-15)^2=225x^{4}\color{magenta}{-450x^2}+225\)
4. \((\color{red}{-8a^5}\color{blue}{+11})(\color{red}{8a^5}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(8a^5)}^2=121-64a^{10}\)
5. \((\color{blue}{-2s}\color{red}{-6})(\color{blue}{-2s}\color{red}{+6})=\color{blue}{(-2s)}^2-\color{red}{(-6)}^2=4s^2-36\)
6. \((s-9)^2=s^2+\color{magenta}{2.s.(-9)}+(-9)^2=s^2\color{magenta}{-18s}+81\)
7. \((p-14)(p-14)=(p-14)^2=p^2+\color{magenta}{2.p.(-14)}+(-14)^2=p^2\color{magenta}{-28p}+196\)
8. \((\color{blue}{12b^2}\color{red}{+9y})(\color{blue}{12b^2}\color{red}{-9y})=\color{blue}{(12b^2)}^2-\color{red}{(9y)}^2=144b^{4}-81y^2\)
9. \((\color{red}{-4x^4}\color{blue}{+4})(\color{red}{4x^4}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(4x^4)}^2=16-16x^{8}\)
10. \((\color{blue}{x}\color{red}{+7})(\color{blue}{x}\color{red}{-7})=\color{blue}{x}^2-\color{red}{7}^2=x^2-49\)
11. \((y-15)(y-15)=(y-15)^2=y^2+\color{magenta}{2.y.(-15)}+(-15)^2=y^2\color{magenta}{-30y}+225\)
12. \((\color{blue}{13y^2}\color{red}{+1})(\color{blue}{13y^2}\color{red}{-1})=\color{blue}{(13y^2)}^2-\color{red}{1}^2=169y^{4}-1\)