Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{16b}\color{red}{-11})(\color{blue}{16b}\color{red}{+11})=\color{blue}{(16b)}^2-\color{red}{(-11)}^2=256b^2-121\)
2. \((-10q+16)(-10q+16)=(-10q+16)^2=(-10q)^2+\color{magenta}{2.(-10q).16}+16^2=100q^2\color{magenta}{-320q}+256\)
3. \((\color{blue}{14b^5}\color{red}{-12})(\color{blue}{14b^5}\color{red}{+12})=\color{blue}{(14b^5)}^2-\color{red}{(-12)}^2=196b^{10}-144\)
4. \((\color{blue}{-11b^2}\color{red}{+5p})(\color{blue}{-11b^2}\color{red}{-5p})=\color{blue}{(-11b^2)}^2-\color{red}{(5p)}^2=121b^{4}-25p^2\)
5. \((14b^4-5p)^2=(14b^4)^2\color{magenta}{+2.(14b^4).(-5p)}+(-5p)^2=196b^{8}\color{magenta}{-140b^4p}+25p^2\)
6. \((6y^4-5b)(6y^4-5b)=(6y^4-5b)^2=(6y^4)^2\color{magenta}{+2.(6y^4).(-5b)}+(-5b)^2=36y^{8}\color{magenta}{-60by^4}+25b^2\)
7. \((-10q+3)(-10q+3)=(-10q+3)^2=(-10q)^2+\color{magenta}{2.(-10q).3}+3^2=100q^2\color{magenta}{-60q}+9\)
8. \((a+15)^2=a^2+\color{magenta}{2.a.15}+15^2=a^2\color{magenta}{+30a}+225\)
9. \((3s^3-11)^2=(3s^3)^2\color{magenta}{+2.(3s^3).(-11)}+(-11)^2=9s^{6}\color{magenta}{-66s^3}+121\)
10. \((\color{blue}{-9b^4}\color{red}{-14})(\color{blue}{-9b^4}\color{red}{+14})=\color{blue}{(-9b^4)}^2-\color{red}{(-14)}^2=81b^{8}-196\)
11. \((-10y-15)^2=(-10y)^2+\color{magenta}{2.(-10y).(-15)}+(-15)^2=100y^2\color{magenta}{+300y}+225\)
12. \((\color{blue}{p}\color{red}{-8})(\color{blue}{p}\color{red}{+8})=\color{blue}{p}^2-\color{red}{8}^2=p^2-64\)