Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((b+11)(b+11)=(b+11)^2=b^2+\color{magenta}{2.b.11}+11^2=b^2\color{magenta}{+22b}+121\)
2. \((\color{blue}{s}\color{red}{+9})(\color{blue}{s}\color{red}{-9})=\color{blue}{s}^2-\color{red}{9}^2=s^2-81\)
3. \((\color{blue}{14s^2}\color{red}{+8a})(\color{blue}{14s^2}\color{red}{-8a})=\color{blue}{(14s^2)}^2-\color{red}{(8a)}^2=196s^{4}-64a^2\)
4. \((15p^2+16)^2=(15p^2)^2\color{magenta}{+2.(15p^2).16}+16^2=225p^{4}\color{magenta}{+480p^2}+256\)
5. \((\color{red}{14x^3}\color{blue}{+4})(\color{red}{-14x^3}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(14x^3)}^2=16-196x^{6}\)
6. \((b+10)^2=b^2+\color{magenta}{2.b.10}+10^2=b^2\color{magenta}{+20b}+100\)
7. \((\color{blue}{15b^4}\color{red}{+3q})(\color{blue}{15b^4}\color{red}{-3q})=\color{blue}{(15b^4)}^2-\color{red}{(3q)}^2=225b^{8}-9q^2\)
8. \((\color{blue}{-2q^5}\color{red}{-16})(\color{blue}{-2q^5}\color{red}{+16})=\color{blue}{(-2q^5)}^2-\color{red}{(-16)}^2=4q^{10}-256\)
9. \((\color{blue}{-8y^3}\color{red}{+1})(\color{blue}{-8y^3}\color{red}{-1})=\color{blue}{(-8y^3)}^2-\color{red}{1}^2=64y^{6}-1\)
10. \((-6a^4-5)(-6a^4-5)=(-6a^4-5)^2=(-6a^4)^2\color{magenta}{+2.(-6a^4).(-5)}+(-5)^2=36a^{8}\color{magenta}{+60a^4}+25\)
11. \((\color{blue}{4b}\color{red}{-16})(\color{blue}{4b}\color{red}{+16})=\color{blue}{(4b)}^2-\color{red}{(-16)}^2=16b^2-256\)
12. \((16q^5-7)^2=(16q^5)^2\color{magenta}{+2.(16q^5).(-7)}+(-7)^2=256q^{10}\color{magenta}{-224q^5}+49\)