Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{7b^5}\color{blue}{-14})(\color{red}{-7b^5}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(7b^5)}^2=196-49b^{10}\)
2. \((2b^4-4)(2b^4-4)=(2b^4-4)^2=(2b^4)^2\color{magenta}{+2.(2b^4).(-4)}+(-4)^2=4b^{8}\color{magenta}{-16b^4}+16\)
3. \((\color{blue}{a}\color{red}{+3})(\color{blue}{a}\color{red}{-3})=\color{blue}{a}^2-\color{red}{3}^2=a^2-9\)
4. \((x+9)(x+9)=(x+9)^2=x^2+\color{magenta}{2.x.9}+9^2=x^2\color{magenta}{+18x}+81\)
5. \((-12s+16)(-12s+16)=(-12s+16)^2=(-12s)^2+\color{magenta}{2.(-12s).16}+16^2=144s^2\color{magenta}{-384s}+256\)
6. \((\color{red}{15b^2}\color{blue}{-2})(\color{red}{-15b^2}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(15b^2)}^2=4-225b^{4}\)
7. \((\color{blue}{-13q^5}\color{red}{-5b})(\color{blue}{-13q^5}\color{red}{+5b})=\color{blue}{(-13q^5)}^2-\color{red}{(-5b)}^2=169q^{10}-25b^2\)
8. \((\color{blue}{q}\color{red}{-12})(\color{blue}{q}\color{red}{+12})=\color{blue}{q}^2-\color{red}{12}^2=q^2-144\)
9. \((-14b^3+14)^2=(-14b^3)^2\color{magenta}{+2.(-14b^3).14}+14^2=196b^{6}\color{magenta}{-392b^3}+196\)
10. \((-y^3-15x)^2=(-y^3)^2\color{magenta}{+2.(-y^3).(-15x)}+(-15x)^2=y^{6}\color{magenta}{+30xy^3}+225x^2\)
11. \((\color{blue}{6y^2}\color{red}{-9})(\color{blue}{6y^2}\color{red}{+9})=\color{blue}{(6y^2)}^2-\color{red}{(-9)}^2=36y^{4}-81\)
12. \((\color{blue}{b}\color{red}{-8})(\color{blue}{b}\color{red}{+8})=\color{blue}{b}^2-\color{red}{8}^2=b^2-64\)