Merkwaardige producten (MP)

Hoofdmenu Eentje per keer  🖨

Bereken de volgende merkwaardige producten

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

---

Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-5q^4-1)(-5q^4-1)=(-5q^4-1)^2=(-5q^4)^2\color{magenta}{+2.(-5q^4).(-1)}+(-1)^2=25q^{8}\color{magenta}{+10q^4}+1\)
2. \((\color{blue}{b}\color{red}{-13})(\color{blue}{b}\color{red}{+13})=\color{blue}{b}^2-\color{red}{13}^2=b^2-169\)
3. \((\color{blue}{b}\color{red}{+14})(\color{blue}{b}\color{red}{-14})=\color{blue}{b}^2-\color{red}{14}^2=b^2-196\)
4. \((\color{red}{-10q^2}\color{blue}{+10x})(\color{red}{10q^2}\color{blue}{+10x})=\color{blue}{(10x)}^2-\color{red}{(10q^2)}^2=100x^2-100q^{4}\)
5. \((12y-4)^2=(12y)^2+\color{magenta}{2.(12y).(-4)}+(-4)^2=144y^2\color{magenta}{-96y}+16\)
6. \((x-15)^2=x^2+\color{magenta}{2.x.(-15)}+(-15)^2=x^2\color{magenta}{-30x}+225\)
7. \((\color{blue}{9q^5}\color{red}{+10})(\color{blue}{9q^5}\color{red}{-10})=\color{blue}{(9q^5)}^2-\color{red}{10}^2=81q^{10}-100\)
8. \((\color{red}{13b}\color{blue}{-16})(\color{red}{-13b}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(13b)}^2=256-169b^2\)
9. \((\color{blue}{16s}\color{red}{-14})(\color{blue}{16s}\color{red}{+14})=\color{blue}{(16s)}^2-\color{red}{(-14)}^2=256s^2-196\)
10. \((13s^5+11x)(13s^5+11x)=(13s^5+11x)^2=(13s^5)^2\color{magenta}{+2.(13s^5).(11x)}+(11x)^2=169s^{10}\color{magenta}{+286s^5x}+121x^2\)
11. \((-11s^2+3)(-11s^2+3)=(-11s^2+3)^2=(-11s^2)^2\color{magenta}{+2.(-11s^2).3}+3^2=121s^{4}\color{magenta}{-66s^2}+9\)
12. \((-11p^2-1)^2=(-11p^2)^2\color{magenta}{+2.(-11p^2).(-1)}+(-1)^2=121p^{4}\color{magenta}{+22p^2}+1\)