Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-12q^2-p)(-12q^2-p)\)
2. \((16a-7)(16a-7)\)
3. \((-14y^3-3)(14y^3-3)\)
4. \((-2x^5+15)(-2x^5+15)\)
5. \((5s^4-7y)(-5s^4-7y)\)
6. \((10q^5-9b)(-10q^5-9b)\)
7. \((x+2)(x-2)\)
8. \((p-11)(p-11)\)
9. \((a-14)^2\)
10. \((15y^5+15)(15y^5-15)\)
11. \((3x^4-13p)(-3x^4-13p)\)
12. \((-12p^2-3s)(12p^2-3s)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-12q^2-p)(-12q^2-p)=(-12q^2-p)^2=(-12q^2)^2\color{magenta}{+2.(-12q^2).(-p)}+(-p)^2=144q^{4}\color{magenta}{+24pq^2}+1p^2\)
2. \((16a-7)(16a-7)=(16a-7)^2=(16a)^2+\color{magenta}{2.(16a).(-7)}+(-7)^2=256a^2\color{magenta}{-224a}+49\)
3. \((\color{red}{-14y^3}\color{blue}{-3})(\color{red}{14y^3}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(14y^3)}^2=9-196y^{6}\)
4. \((-2x^5+15)(-2x^5+15)=(-2x^5+15)^2=(-2x^5)^2\color{magenta}{+2.(-2x^5).15}+15^2=4x^{10}\color{magenta}{-60x^5}+225\)
5. \((\color{red}{5s^4}\color{blue}{-7y})(\color{red}{-5s^4}\color{blue}{-7y})=\color{blue}{(-7y)}^2-\color{red}{(5s^4)}^2=49y^2-25s^{8}\)
6. \((\color{red}{10q^5}\color{blue}{-9b})(\color{red}{-10q^5}\color{blue}{-9b})=\color{blue}{(-9b)}^2-\color{red}{(10q^5)}^2=81b^2-100q^{10}\)
7. \((\color{blue}{x}\color{red}{+2})(\color{blue}{x}\color{red}{-2})=\color{blue}{x}^2-\color{red}{2}^2=x^2-4\)
8. \((p-11)(p-11)=(p-11)^2=p^2+\color{magenta}{2.p.(-11)}+(-11)^2=p^2\color{magenta}{-22p}+121\)
9. \((a-14)^2=a^2+\color{magenta}{2.a.(-14)}+(-14)^2=a^2\color{magenta}{-28a}+196\)
10. \((\color{blue}{15y^5}\color{red}{+15})(\color{blue}{15y^5}\color{red}{-15})=\color{blue}{(15y^5)}^2-\color{red}{15}^2=225y^{10}-225\)
11. \((\color{red}{3x^4}\color{blue}{-13p})(\color{red}{-3x^4}\color{blue}{-13p})=\color{blue}{(-13p)}^2-\color{red}{(3x^4)}^2=169p^2-9x^{8}\)
12. \((\color{red}{-12p^2}\color{blue}{-3s})(\color{red}{12p^2}\color{blue}{-3s})=\color{blue}{(-3s)}^2-\color{red}{(12p^2)}^2=9s^2-144p^{4}\)