Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{s}\color{red}{+15})(\color{blue}{s}\color{red}{-15})=\color{blue}{s}^2-\color{red}{15}^2=s^2-225\)
2. \((\color{red}{13b^4}\color{blue}{+7})(\color{red}{-13b^4}\color{blue}{+7})=\color{blue}{7}^2-\color{red}{(13b^4)}^2=49-169b^{8}\)
3. \((4b^5+7q)^2=(4b^5)^2\color{magenta}{+2.(4b^5).(7q)}+(7q)^2=16b^{10}\color{magenta}{+56b^5q}+49q^2\)
4. \((\color{blue}{q}\color{red}{-14})(\color{blue}{q}\color{red}{+14})=\color{blue}{q}^2-\color{red}{14}^2=q^2-196\)
5. \((10p^2+7)^2=(10p^2)^2\color{magenta}{+2.(10p^2).7}+7^2=100p^{4}\color{magenta}{+140p^2}+49\)
6. \((\color{blue}{11s}\color{red}{-1})(\color{blue}{11s}\color{red}{+1})=\color{blue}{(11s)}^2-\color{red}{(-1)}^2=121s^2-1\)
7. \((x-6)^2=x^2+\color{magenta}{2.x.(-6)}+(-6)^2=x^2\color{magenta}{-12x}+36\)
8. \((\color{red}{11x^4}\color{blue}{+10y})(\color{red}{-11x^4}\color{blue}{+10y})=\color{blue}{(10y)}^2-\color{red}{(11x^4)}^2=100y^2-121x^{8}\)
9. \((\color{blue}{3y}\color{red}{-4})(\color{blue}{3y}\color{red}{+4})=\color{blue}{(3y)}^2-\color{red}{(-4)}^2=9y^2-16\)
10. \((\color{red}{-15b^4}\color{blue}{+3})(\color{red}{15b^4}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(15b^4)}^2=9-225b^{8}\)
11. \((10q^2+5a)^2=(10q^2)^2\color{magenta}{+2.(10q^2).(5a)}+(5a)^2=100q^{4}\color{magenta}{+100aq^2}+25a^2\)
12. \((16y+16)^2=(16y)^2+\color{magenta}{2.(16y).16}+16^2=256y^2\color{magenta}{+512y}+256\)