Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{x}\color{red}{-4})(\color{blue}{x}\color{red}{+4})=\color{blue}{x}^2-\color{red}{4}^2=x^2-16\)
2. \((\color{red}{-12s^5}\color{blue}{-12p})(\color{red}{12s^5}\color{blue}{-12p})=\color{blue}{(-12p)}^2-\color{red}{(12s^5)}^2=144p^2-144s^{10}\)
3. \((\color{blue}{11a^5}\color{red}{-2y})(\color{blue}{11a^5}\color{red}{+2y})=\color{blue}{(11a^5)}^2-\color{red}{(-2y)}^2=121a^{10}-4y^2\)
4. \((-y^5+b)^2=(-y^5)^2\color{magenta}{+2.(-y^5).(b)}+(b)^2=y^{10}\color{magenta}{-2by^5}+1b^2\)
5. \((-13x^4+16)^2=(-13x^4)^2\color{magenta}{+2.(-13x^4).16}+16^2=169x^{8}\color{magenta}{-416x^4}+256\)
6. \((-16p^2-13)(-16p^2-13)=(-16p^2-13)^2=(-16p^2)^2\color{magenta}{+2.(-16p^2).(-13)}+(-13)^2=256p^{4}\color{magenta}{+416p^2}+169\)
7. \((\color{red}{16x^3}\color{blue}{-5b})(\color{red}{-16x^3}\color{blue}{-5b})=\color{blue}{(-5b)}^2-\color{red}{(16x^3)}^2=25b^2-256x^{6}\)
8. \((13x^3+16s)(13x^3+16s)=(13x^3+16s)^2=(13x^3)^2\color{magenta}{+2.(13x^3).(16s)}+(16s)^2=169x^{6}\color{magenta}{+416sx^3}+256s^2\)
9. \((7y^3-15q)(7y^3-15q)=(7y^3-15q)^2=(7y^3)^2\color{magenta}{+2.(7y^3).(-15q)}+(-15q)^2=49y^{6}\color{magenta}{-210qy^3}+225q^2\)
10. \((\color{red}{12p}\color{blue}{+11})(\color{red}{-12p}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(12p)}^2=121-144p^2\)
11. \((\color{blue}{-8p}\color{red}{-7})(\color{blue}{-8p}\color{red}{+7})=\color{blue}{(-8p)}^2-\color{red}{(-7)}^2=64p^2-49\)
12. \((16a^5-13s)(16a^5-13s)=(16a^5-13s)^2=(16a^5)^2\color{magenta}{+2.(16a^5).(-13s)}+(-13s)^2=256a^{10}\color{magenta}{-416a^5s}+169s^2\)