Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-7b^2-11q)(-7b^2-11q)=(-7b^2-11q)^2=(-7b^2)^2\color{magenta}{+2.(-7b^2).(-11q)}+(-11q)^2=49b^{4}\color{magenta}{+154b^2q}+121q^2\)
2. \((\color{blue}{-p^3}\color{red}{+3})(\color{blue}{-p^3}\color{red}{-3})=\color{blue}{(-p^3)}^2-\color{red}{3}^2=p^{6}-9\)
3. \((s+15)^2=s^2+\color{magenta}{2.s.15}+15^2=s^2\color{magenta}{+30s}+225\)
4. \((\color{red}{10x^2}\color{blue}{-5b})(\color{red}{-10x^2}\color{blue}{-5b})=\color{blue}{(-5b)}^2-\color{red}{(10x^2)}^2=25b^2-100x^{4}\)
5. \((\color{blue}{b}\color{red}{+9})(\color{blue}{b}\color{red}{-9})=\color{blue}{b}^2-\color{red}{9}^2=b^2-81\)
6. \((\color{red}{12p^4}\color{blue}{+15a})(\color{red}{-12p^4}\color{blue}{+15a})=\color{blue}{(15a)}^2-\color{red}{(12p^4)}^2=225a^2-144p^{8}\)
7. \((\color{blue}{b}\color{red}{-4})(\color{blue}{b}\color{red}{+4})=\color{blue}{b}^2-\color{red}{4}^2=b^2-16\)
8. \((a^5-3)^2=(a^5)^2\color{magenta}{+2.(a^5).(-3)}+(-3)^2=1a^{10}\color{magenta}{-6a^5}+9\)
9. \((-y-6)(-y-6)=(-y-6)^2=(-y)^2+\color{magenta}{2.(-y).(-6)}+(-6)^2=y^2\color{magenta}{+12y}+36\)
10. \((\color{red}{9a}\color{blue}{+12})(\color{red}{-9a}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(9a)}^2=144-81a^2\)
11. \((4b^2-11)^2=(4b^2)^2\color{magenta}{+2.(4b^2).(-11)}+(-11)^2=16b^{4}\color{magenta}{-88b^2}+121\)
12. \((x-7)^2=x^2+\color{magenta}{2.x.(-7)}+(-7)^2=x^2\color{magenta}{-14x}+49\)