Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-3p}\color{red}{-9})(\color{blue}{-3p}\color{red}{+9})=\color{blue}{(-3p)}^2-\color{red}{(-9)}^2=9p^2-81\)
2. \((q-4)^2=q^2+\color{magenta}{2.q.(-4)}+(-4)^2=q^2\color{magenta}{-8q}+16\)
3. \((15a^2-5)^2=(15a^2)^2\color{magenta}{+2.(15a^2).(-5)}+(-5)^2=225a^{4}\color{magenta}{-150a^2}+25\)
4. \((\color{blue}{9b^3}\color{red}{-6})(\color{blue}{9b^3}\color{red}{+6})=\color{blue}{(9b^3)}^2-\color{red}{(-6)}^2=81b^{6}-36\)
5. \((9a^4+10)(9a^4+10)=(9a^4+10)^2=(9a^4)^2\color{magenta}{+2.(9a^4).10}+10^2=81a^{8}\color{magenta}{+180a^4}+100\)
6. \((\color{red}{3q}\color{blue}{-4})(\color{red}{-3q}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(3q)}^2=16-9q^2\)
7. \((x+5)^2=x^2+\color{magenta}{2.x.5}+5^2=x^2\color{magenta}{+10x}+25\)
8. \((x+12)^2=x^2+\color{magenta}{2.x.12}+12^2=x^2\color{magenta}{+24x}+144\)
9. \((\color{blue}{-7s^4}\color{red}{-13})(\color{blue}{-7s^4}\color{red}{+13})=\color{blue}{(-7s^4)}^2-\color{red}{(-13)}^2=49s^{8}-169\)
10. \((7q^2-10y)^2=(7q^2)^2\color{magenta}{+2.(7q^2).(-10y)}+(-10y)^2=49q^{4}\color{magenta}{-140q^2y}+100y^2\)
11. \((\color{red}{-13x^5}\color{blue}{+15b})(\color{red}{13x^5}\color{blue}{+15b})=\color{blue}{(15b)}^2-\color{red}{(13x^5)}^2=225b^2-169x^{10}\)
12. \((\color{red}{11q^4}\color{blue}{+10y})(\color{red}{-11q^4}\color{blue}{+10y})=\color{blue}{(10y)}^2-\color{red}{(11q^4)}^2=100y^2-121q^{8}\)