Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-7y^4-6x)(-7y^4-6x)=(-7y^4-6x)^2=(-7y^4)^2\color{magenta}{+2.(-7y^4).(-6x)}+(-6x)^2=49y^{8}\color{magenta}{+84xy^4}+36x^2\)
2. \((\color{blue}{-8b^2}\color{red}{-11x})(\color{blue}{-8b^2}\color{red}{+11x})=\color{blue}{(-8b^2)}^2-\color{red}{(-11x)}^2=64b^{4}-121x^2\)
3. \((s+15)^2=s^2+\color{magenta}{2.s.15}+15^2=s^2\color{magenta}{+30s}+225\)
4. \((\color{blue}{x}\color{red}{-15})(\color{blue}{x}\color{red}{+15})=\color{blue}{x}^2-\color{red}{15}^2=x^2-225\)
5. \((\color{blue}{11x}\color{red}{+3})(\color{blue}{11x}\color{red}{-3})=\color{blue}{(11x)}^2-\color{red}{(3)}^2=121x^2-9\)
6. \((a+4)^2=a^2+\color{magenta}{2.a.4}+4^2=a^2\color{magenta}{+8a}+16\)
7. \((5p^3+9)(5p^3+9)=(5p^3+9)^2=(5p^3)^2\color{magenta}{+2.(5p^3).9}+9^2=25p^{6}\color{magenta}{+90p^3}+81\)
8. \((p^4-2a)^2=(p^4)^2\color{magenta}{+2.(p^4).(-2a)}+(-2a)^2=p^{8}\color{magenta}{-4ap^4}+4a^2\)
9. \((\color{blue}{-3s^5}\color{red}{-5})(\color{blue}{-3s^5}\color{red}{+5})=\color{blue}{(-3s^5)}^2-\color{red}{(-5)}^2=9s^{10}-25\)
10. \((14a^2+9p)^2=(14a^2)^2\color{magenta}{+2.(14a^2).(9p)}+(9p)^2=196a^{4}\color{magenta}{+252a^2p}+81p^2\)
11. \((\color{blue}{-p^5}\color{red}{+14})(\color{blue}{-p^5}\color{red}{-14})=\color{blue}{(-p^5)}^2-\color{red}{14}^2=p^{10}-196\)
12. \((-2b^2+10s)(-2b^2+10s)=(-2b^2+10s)^2=(-2b^2)^2\color{magenta}{+2.(-2b^2).(10s)}+(10s)^2=4b^{4}\color{magenta}{-40b^2s}+100s^2\)