Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p-5)(p-5)=(p-5)^2=p^2+\color{magenta}{2.p.(-5)}+(-5)^2=p^2\color{magenta}{-10p}+25\)
2. \((-3q-6)^2=(-3q)^2+\color{magenta}{2.(-3q).(-6)}+(-6)^2=9q^2\color{magenta}{+36q}+36\)
3. \((11p^2+9q)^2=(11p^2)^2\color{magenta}{+2.(11p^2).(9q)}+(9q)^2=121p^{4}\color{magenta}{+198p^2q}+81q^2\)
4. \((-5a+7)^2=(-5a)^2+\color{magenta}{2.(-5a).7}+7^2=25a^2\color{magenta}{-70a}+49\)
5. \((\color{red}{-3s^2}\color{blue}{+2q})(\color{red}{3s^2}\color{blue}{+2q})=\color{blue}{(2q)}^2-\color{red}{(3s^2)}^2=4q^2-9s^{4}\)
6. \((8y^2-9)(8y^2-9)=(8y^2-9)^2=(8y^2)^2\color{magenta}{+2.(8y^2).(-9)}+(-9)^2=64y^{4}\color{magenta}{-144y^2}+81\)
7. \((\color{red}{7a^3}\color{blue}{+13})(\color{red}{-7a^3}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(7a^3)}^2=169-49a^{6}\)
8. \((\color{blue}{-12q^2}\color{red}{-7s})(\color{blue}{-12q^2}\color{red}{+7s})=\color{blue}{(-12q^2)}^2-\color{red}{(-7s)}^2=144q^{4}-49s^2\)
9. \((3y-15)(3y-15)=(3y-15)^2=(3y)^2+\color{magenta}{2.(3y).(-15)}+(-15)^2=9y^2\color{magenta}{-90y}+225\)
10. \((\color{red}{-7q^5}\color{blue}{-y})(\color{red}{7q^5}\color{blue}{-y})=\color{blue}{(-1y)}^2-\color{red}{(7q^5)}^2=1y^2-49q^{10}\)
11. \((\color{red}{7p}\color{blue}{-11})(\color{red}{-7p}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(7p)}^2=121-49p^2\)
12. \((\color{red}{-b^2}\color{blue}{-3q})(\color{red}{b^2}\color{blue}{-3q})=\color{blue}{(-3q)}^2-\color{red}{(b^2)}^2=9q^2-b^{4}\)