Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-10p^3}\color{blue}{+16})(\color{red}{10p^3}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(10p^3)}^2=256-100p^{6}\)
2. \((\color{blue}{y}\color{red}{-11})(\color{blue}{y}\color{red}{+11})=\color{blue}{y}^2-\color{red}{11}^2=y^2-121\)
3. \((-15x^4+11a)^2=(-15x^4)^2\color{magenta}{+2.(-15x^4).(11a)}+(11a)^2=225x^{8}\color{magenta}{-330ax^4}+121a^2\)
4. \((\color{blue}{12x}\color{red}{+7})(\color{blue}{12x}\color{red}{-7})=\color{blue}{(12x)}^2-\color{red}{(7)}^2=144x^2-49\)
5. \((10q^4-2a)^2=(10q^4)^2\color{magenta}{+2.(10q^4).(-2a)}+(-2a)^2=100q^{8}\color{magenta}{-40aq^4}+4a^2\)
6. \((\color{red}{15b^2}\color{blue}{+7})(\color{red}{-15b^2}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(15b^2)}^2=49-225b^{4}\)
7. \((-8a^5+6p)^2=(-8a^5)^2\color{magenta}{+2.(-8a^5).(6p)}+(6p)^2=64a^{10}\color{magenta}{-96a^5p}+36p^2\)
8. \((\color{red}{13b^3}\color{blue}{+8s})(\color{red}{-13b^3}\color{blue}{+8s})=\color{blue}{(8s)}^2-\color{red}{(13b^3)}^2=64s^2-169b^{6}\)
9. \((-9q^5+7)(-9q^5+7)=(-9q^5+7)^2=(-9q^5)^2\color{magenta}{+2.(-9q^5).7}+7^2=81q^{10}\color{magenta}{-126q^5}+49\)
10. \((\color{blue}{15x^5}\color{red}{-13b})(\color{blue}{15x^5}\color{red}{+13b})=\color{blue}{(15x^5)}^2-\color{red}{(-13b)}^2=225x^{10}-169b^2\)
11. \((3a^4+7p)(3a^4+7p)=(3a^4+7p)^2=(3a^4)^2\color{magenta}{+2.(3a^4).(7p)}+(7p)^2=9a^{8}\color{magenta}{+42a^4p}+49p^2\)
12. \((a-14)^2=a^2+\color{magenta}{2.a.(-14)}+(-14)^2=a^2\color{magenta}{-28a}+196\)