Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-11s^5}\color{blue}{-4x})(\color{red}{11s^5}\color{blue}{-4x})=\color{blue}{(-4x)}^2-\color{red}{(11s^5)}^2=16x^2-121s^{10}\)
2. \((\color{blue}{x}\color{red}{+6})(\color{blue}{x}\color{red}{-6})=\color{blue}{x}^2-\color{red}{6}^2=x^2-36\)
3. \((\color{blue}{16b^3}\color{red}{-6a})(\color{blue}{16b^3}\color{red}{+6a})=\color{blue}{(16b^3)}^2-\color{red}{(-6a)}^2=256b^{6}-36a^2\)
4. \((\color{red}{-10x^2}\color{blue}{-5p})(\color{red}{10x^2}\color{blue}{-5p})=\color{blue}{(-5p)}^2-\color{red}{(10x^2)}^2=25p^2-100x^{4}\)
5. \((12a^2-14y)(12a^2-14y)=(12a^2-14y)^2=(12a^2)^2\color{magenta}{+2.(12a^2).(-14y)}+(-14y)^2=144a^{4}\color{magenta}{-336a^2y}+196y^2\)
6. \((3x+16)^2=(3x)^2+\color{magenta}{2.(3x).16}+16^2=9x^2\color{magenta}{+96x}+256\)
7. \((13s^5-3x)(13s^5-3x)=(13s^5-3x)^2=(13s^5)^2\color{magenta}{+2.(13s^5).(-3x)}+(-3x)^2=169s^{10}\color{magenta}{-78s^5x}+9x^2\)
8. \((\color{blue}{b}\color{red}{+4})(\color{blue}{b}\color{red}{-4})=\color{blue}{b}^2-\color{red}{4}^2=b^2-16\)
9. \((\color{blue}{x}\color{red}{+1})(\color{blue}{x}\color{red}{-1})=\color{blue}{x}^2-\color{red}{1}^2=x^2-1\)
10. \((10a^3-6q)(10a^3-6q)=(10a^3-6q)^2=(10a^3)^2\color{magenta}{+2.(10a^3).(-6q)}+(-6q)^2=100a^{6}\color{magenta}{-120a^3q}+36q^2\)
11. \((s-14)^2=s^2+\color{magenta}{2.s.(-14)}+(-14)^2=s^2\color{magenta}{-28s}+196\)
12. \((q-5)^2=q^2+\color{magenta}{2.q.(-5)}+(-5)^2=q^2\color{magenta}{-10q}+25\)