Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-8x}\color{blue}{+6})(\color{red}{8x}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(8x)}^2=36-64x^2\)
2. \((\color{blue}{-9q^3}\color{red}{-14y})(\color{blue}{-9q^3}\color{red}{+14y})=\color{blue}{(-9q^3)}^2-\color{red}{(-14y)}^2=81q^{6}-196y^2\)
3. \((-2a+6)^2=(-2a)^2+\color{magenta}{2.(-2a).6}+6^2=4a^2\color{magenta}{-24a}+36\)
4. \((\color{blue}{-6s^2}\color{red}{-13p})(\color{blue}{-6s^2}\color{red}{+13p})=\color{blue}{(-6s^2)}^2-\color{red}{(-13p)}^2=36s^{4}-169p^2\)
5. \((\color{blue}{-3a}\color{red}{-16})(\color{blue}{-3a}\color{red}{+16})=\color{blue}{(-3a)}^2-\color{red}{(-16)}^2=9a^2-256\)
6. \((\color{blue}{-13x^4}\color{red}{-1})(\color{blue}{-13x^4}\color{red}{+1})=\color{blue}{(-13x^4)}^2-\color{red}{(-1)}^2=169x^{8}-1\)
7. \((-6q^5-2)^2=(-6q^5)^2\color{magenta}{+2.(-6q^5).(-2)}+(-2)^2=36q^{10}\color{magenta}{+24q^5}+4\)
8. \((\color{blue}{s}\color{red}{+15})(\color{blue}{s}\color{red}{-15})=\color{blue}{s}^2-\color{red}{15}^2=s^2-225\)
9. \((\color{blue}{16q^5}\color{red}{-16x})(\color{blue}{16q^5}\color{red}{+16x})=\color{blue}{(16q^5)}^2-\color{red}{(-16x)}^2=256q^{10}-256x^2\)
10. \((\color{blue}{q}\color{red}{-9})(\color{blue}{q}\color{red}{+9})=\color{blue}{q}^2-\color{red}{9}^2=q^2-81\)
11. \((-6p^4+14q)^2=(-6p^4)^2\color{magenta}{+2.(-6p^4).(14q)}+(14q)^2=36p^{8}\color{magenta}{-168p^4q}+196q^2\)
12. \((-12y^5-2a)^2=(-12y^5)^2\color{magenta}{+2.(-12y^5).(-2a)}+(-2a)^2=144y^{10}\color{magenta}{+48ay^5}+4a^2\)