Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{2q}\color{red}{-1})(\color{blue}{2q}\color{red}{+1})=\color{blue}{(2q)}^2-\color{red}{(-1)}^2=4q^2-1\)
2. \((\color{blue}{2q^4}\color{red}{-7})(\color{blue}{2q^4}\color{red}{+7})=\color{blue}{(2q^4)}^2-\color{red}{(-7)}^2=4q^{8}-49\)
3. \((15p^3+10s)^2=(15p^3)^2\color{magenta}{+2.(15p^3).(10s)}+(10s)^2=225p^{6}\color{magenta}{+300p^3s}+100s^2\)
4. \((-13p+15)^2=(-13p)^2+\color{magenta}{2.(-13p).15}+15^2=169p^2\color{magenta}{-390p}+225\)
5. \((9s^2+12)(9s^2+12)=(9s^2+12)^2=(9s^2)^2\color{magenta}{+2.(9s^2).12}+12^2=81s^{4}\color{magenta}{+216s^2}+144\)
6. \((7p^3+7s)^2=(7p^3)^2\color{magenta}{+2.(7p^3).(7s)}+(7s)^2=49p^{6}\color{magenta}{+98p^3s}+49s^2\)
7. \((\color{red}{-15x^2}\color{blue}{-7})(\color{red}{15x^2}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(15x^2)}^2=49-225x^{4}\)
8. \((\color{red}{-12x}\color{blue}{-4})(\color{red}{12x}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(12x)}^2=16-144x^2\)
9. \((15y^2-14p)^2=(15y^2)^2\color{magenta}{+2.(15y^2).(-14p)}+(-14p)^2=225y^{4}\color{magenta}{-420py^2}+196p^2\)
10. \((-8p+8)(-8p+8)=(-8p+8)^2=(-8p)^2+\color{magenta}{2.(-8p).8}+8^2=64p^2\color{magenta}{-128p}+64\)
11. \((\color{blue}{-11y^2}\color{red}{+6})(\color{blue}{-11y^2}\color{red}{-6})=\color{blue}{(-11y^2)}^2-\color{red}{6}^2=121y^{4}-36\)
12. \((\color{blue}{y}\color{red}{+12})(\color{blue}{y}\color{red}{-12})=\color{blue}{y}^2-\color{red}{12}^2=y^2-144\)