Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-p-12)(-p-12)=(-p-12)^2=(-p)^2+\color{magenta}{2.(-p).(-12)}+(-12)^2=p^2\color{magenta}{+24p}+144\)
2. \((\color{blue}{x}\color{red}{+10})(\color{blue}{x}\color{red}{-10})=\color{blue}{x}^2-\color{red}{10}^2=x^2-100\)
3. \((12x^2-13p)(12x^2-13p)=(12x^2-13p)^2=(12x^2)^2\color{magenta}{+2.(12x^2).(-13p)}+(-13p)^2=144x^{4}\color{magenta}{-312px^2}+169p^2\)
4. \((\color{red}{-8s}\color{blue}{+5})(\color{red}{8s}\color{blue}{+5})=\color{blue}{5}^2-\color{red}{(8s)}^2=25-64s^2\)
5. \((a-6)^2=a^2+\color{magenta}{2.a.(-6)}+(-6)^2=a^2\color{magenta}{-12a}+36\)
6. \((\color{blue}{-2a^3}\color{red}{-7s})(\color{blue}{-2a^3}\color{red}{+7s})=\color{blue}{(-2a^3)}^2-\color{red}{(-7s)}^2=4a^{6}-49s^2\)
7. \((\color{red}{5q}\color{blue}{-2})(\color{red}{-5q}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(5q)}^2=4-25q^2\)
8. \((\color{red}{-8x^5}\color{blue}{+4p})(\color{red}{8x^5}\color{blue}{+4p})=\color{blue}{(4p)}^2-\color{red}{(8x^5)}^2=16p^2-64x^{10}\)
9. \((\color{red}{7p}\color{blue}{+9})(\color{red}{-7p}\color{blue}{+9})=\color{blue}{9}^2-\color{red}{(7p)}^2=81-49p^2\)
10. \((11p^4-s)(11p^4-s)=(11p^4-s)^2=(11p^4)^2\color{magenta}{+2.(11p^4).(-s)}+(-s)^2=121p^{8}\color{magenta}{-22p^4s}+1s^2\)
11. \((9b^3-14q)^2=(9b^3)^2\color{magenta}{+2.(9b^3).(-14q)}+(-14q)^2=81b^{6}\color{magenta}{-252b^3q}+196q^2\)
12. \((-11b^3-9p)(-11b^3-9p)=(-11b^3-9p)^2=(-11b^3)^2\color{magenta}{+2.(-11b^3).(-9p)}+(-9p)^2=121b^{6}\color{magenta}{+198b^3p}+81p^2\)