Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((9s^4-2x)(9s^4-2x)=(9s^4-2x)^2=(9s^4)^2\color{magenta}{+2.(9s^4).(-2x)}+(-2x)^2=81s^{8}\color{magenta}{-36s^4x}+4x^2\)
2. \((-12q^5-16)^2=(-12q^5)^2\color{magenta}{+2.(-12q^5).(-16)}+(-16)^2=144q^{10}\color{magenta}{+384q^5}+256\)
3. \((\color{red}{11b}\color{blue}{+10})(\color{red}{-11b}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(11b)}^2=100-121b^2\)
4. \((s-9)^2=s^2+\color{magenta}{2.s.(-9)}+(-9)^2=s^2\color{magenta}{-18s}+81\)
5. \((\color{blue}{-5x}\color{red}{+7})(\color{blue}{-5x}\color{red}{-7})=\color{blue}{(-5x)}^2-\color{red}{(7)}^2=25x^2-49\)
6. \((-14a^2-9)(-14a^2-9)=(-14a^2-9)^2=(-14a^2)^2\color{magenta}{+2.(-14a^2).(-9)}+(-9)^2=196a^{4}\color{magenta}{+252a^2}+81\)
7. \((\color{red}{-9b}\color{blue}{-2})(\color{red}{9b}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(9b)}^2=4-81b^2\)
8. \((-3b+7)(-3b+7)=(-3b+7)^2=(-3b)^2+\color{magenta}{2.(-3b).7}+7^2=9b^2\color{magenta}{-42b}+49\)
9. \((-2s-9)^2=(-2s)^2+\color{magenta}{2.(-2s).(-9)}+(-9)^2=4s^2\color{magenta}{+36s}+81\)
10. \((\color{blue}{-7s}\color{red}{+13})(\color{blue}{-7s}\color{red}{-13})=\color{blue}{(-7s)}^2-\color{red}{(13)}^2=49s^2-169\)
11. \((\color{blue}{12y^5}\color{red}{-12p})(\color{blue}{12y^5}\color{red}{+12p})=\color{blue}{(12y^5)}^2-\color{red}{(-12p)}^2=144y^{10}-144p^2\)
12. \((s+5)(s+5)=(s+5)^2=s^2+\color{magenta}{2.s.5}+5^2=s^2\color{magenta}{+10s}+25\)