Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{14s}\color{red}{-6})(\color{blue}{14s}\color{red}{+6})=\color{blue}{(14s)}^2-\color{red}{(-6)}^2=196s^2-36\)
2. \((\color{blue}{-2a^4}\color{red}{-4})(\color{blue}{-2a^4}\color{red}{+4})=\color{blue}{(-2a^4)}^2-\color{red}{(-4)}^2=4a^{8}-16\)
3. \((\color{red}{-8q}\color{blue}{-5})(\color{red}{8q}\color{blue}{-5})=\color{blue}{(-5)}^2-\color{red}{(8q)}^2=25-64q^2\)
4. \((\color{blue}{q}\color{red}{+4})(\color{blue}{q}\color{red}{-4})=\color{blue}{q}^2-\color{red}{4}^2=q^2-16\)
5. \((b-2)(b-2)=(b-2)^2=b^2+\color{magenta}{2.b.(-2)}+(-2)^2=b^2\color{magenta}{-4b}+4\)
6. \((-7p^4-3a)^2=(-7p^4)^2\color{magenta}{+2.(-7p^4).(-3a)}+(-3a)^2=49p^{8}\color{magenta}{+42ap^4}+9a^2\)
7. \((x-8)(x-8)=(x-8)^2=x^2+\color{magenta}{2.x.(-8)}+(-8)^2=x^2\color{magenta}{-16x}+64\)
8. \((\color{red}{15y^3}\color{blue}{-6x})(\color{red}{-15y^3}\color{blue}{-6x})=\color{blue}{(-6x)}^2-\color{red}{(15y^3)}^2=36x^2-225y^{6}\)
9. \((11y-6)(11y-6)=(11y-6)^2=(11y)^2+\color{magenta}{2.(11y).(-6)}+(-6)^2=121y^2\color{magenta}{-132y}+36\)
10. \((\color{red}{13a^3}\color{blue}{-11})(\color{red}{-13a^3}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(13a^3)}^2=121-169a^{6}\)
11. \((-7a+11)^2=(-7a)^2+\color{magenta}{2.(-7a).11}+11^2=49a^2\color{magenta}{-154a}+121\)
12. \((-5p-2)(-5p-2)=(-5p-2)^2=(-5p)^2+\color{magenta}{2.(-5p).(-2)}+(-2)^2=25p^2\color{magenta}{+20p}+4\)