Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-2q^3+15p)(-2q^3+15p)=(-2q^3+15p)^2=(-2q^3)^2\color{magenta}{+2.(-2q^3).(15p)}+(15p)^2=4q^{6}\color{magenta}{-60pq^3}+225p^2\)
2. \((11s^2+5)(11s^2+5)=(11s^2+5)^2=(11s^2)^2\color{magenta}{+2.(11s^2).5}+5^2=121s^{4}\color{magenta}{+110s^2}+25\)
3. \((\color{blue}{-13x^4}\color{red}{-10})(\color{blue}{-13x^4}\color{red}{+10})=\color{blue}{(-13x^4)}^2-\color{red}{(-10)}^2=169x^{8}-100\)
4. \((\color{blue}{-3s}\color{red}{-5})(\color{blue}{-3s}\color{red}{+5})=\color{blue}{(-3s)}^2-\color{red}{(-5)}^2=9s^2-25\)
5. \((\color{blue}{b}\color{red}{+1})(\color{blue}{b}\color{red}{-1})=\color{blue}{b}^2-\color{red}{1}^2=b^2-1\)
6. \((12s^5+12)(12s^5+12)=(12s^5+12)^2=(12s^5)^2\color{magenta}{+2.(12s^5).12}+12^2=144s^{10}\color{magenta}{+288s^5}+144\)
7. \((3q^5+8a)(3q^5+8a)=(3q^5+8a)^2=(3q^5)^2\color{magenta}{+2.(3q^5).(8a)}+(8a)^2=9q^{10}\color{magenta}{+48aq^5}+64a^2\)
8. \((-12a^3+10)^2=(-12a^3)^2\color{magenta}{+2.(-12a^3).10}+10^2=144a^{6}\color{magenta}{-240a^3}+100\)
9. \((3a-9)(3a-9)=(3a-9)^2=(3a)^2+\color{magenta}{2.(3a).(-9)}+(-9)^2=9a^2\color{magenta}{-54a}+81\)
10. \((3p^3+15b)^2=(3p^3)^2\color{magenta}{+2.(3p^3).(15b)}+(15b)^2=9p^{6}\color{magenta}{+90bp^3}+225b^2\)
11. \((\color{blue}{7q^5}\color{red}{-9s})(\color{blue}{7q^5}\color{red}{+9s})=\color{blue}{(7q^5)}^2-\color{red}{(-9s)}^2=49q^{10}-81s^2\)
12. \((-16y^3+9)^2=(-16y^3)^2\color{magenta}{+2.(-16y^3).9}+9^2=256y^{6}\color{magenta}{-288y^3}+81\)