Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-7b^2+1)^2=(-7b^2)^2\color{magenta}{+2.(-7b^2).1}+1^2=49b^{4}\color{magenta}{-14b^2}+1\)
2. \((\color{blue}{p}\color{red}{-14})(\color{blue}{p}\color{red}{+14})=\color{blue}{p}^2-\color{red}{14}^2=p^2-196\)
3. \((\color{blue}{y}\color{red}{-5})(\color{blue}{y}\color{red}{+5})=\color{blue}{y}^2-\color{red}{5}^2=y^2-25\)
4. \((\color{blue}{14a^3}\color{red}{-12})(\color{blue}{14a^3}\color{red}{+12})=\color{blue}{(14a^3)}^2-\color{red}{(-12)}^2=196a^{6}-144\)
5. \((\color{red}{14y^3}\color{blue}{+3a})(\color{red}{-14y^3}\color{blue}{+3a})=\color{blue}{(3a)}^2-\color{red}{(14y^3)}^2=9a^2-196y^{6}\)
6. \((b+15)^2=b^2+\color{magenta}{2.b.15}+15^2=b^2\color{magenta}{+30b}+225\)
7. \((a+2)(a+2)=(a+2)^2=a^2+\color{magenta}{2.a.2}+2^2=a^2\color{magenta}{+4a}+4\)
8. \((b-8)^2=b^2+\color{magenta}{2.b.(-8)}+(-8)^2=b^2\color{magenta}{-16b}+64\)
9. \((-15y-14)^2=(-15y)^2+\color{magenta}{2.(-15y).(-14)}+(-14)^2=225y^2\color{magenta}{+420y}+196\)
10. \((\color{blue}{-5s^2}\color{red}{+8})(\color{blue}{-5s^2}\color{red}{-8})=\color{blue}{(-5s^2)}^2-\color{red}{8}^2=25s^{4}-64\)
11. \((-15b+3)(-15b+3)=(-15b+3)^2=(-15b)^2+\color{magenta}{2.(-15b).3}+3^2=225b^2\color{magenta}{-90b}+9\)
12. \((-14y^5-7)(-14y^5-7)=(-14y^5-7)^2=(-14y^5)^2\color{magenta}{+2.(-14y^5).(-7)}+(-7)^2=196y^{10}\color{magenta}{+196y^5}+49\)