Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-12s^2-12b)^2=(-12s^2)^2\color{magenta}{+2.(-12s^2).(-12b)}+(-12b)^2=144s^{4}\color{magenta}{+288bs^2}+144b^2\)
2. \((\color{blue}{5a}\color{red}{+7})(\color{blue}{5a}\color{red}{-7})=\color{blue}{(5a)}^2-\color{red}{(7)}^2=25a^2-49\)
3. \((\color{blue}{-9a}\color{red}{+2})(\color{blue}{-9a}\color{red}{-2})=\color{blue}{(-9a)}^2-\color{red}{(2)}^2=81a^2-4\)
4. \((-10y-12)(-10y-12)=(-10y-12)^2=(-10y)^2+\color{magenta}{2.(-10y).(-12)}+(-12)^2=100y^2\color{magenta}{+240y}+144\)
5. \((q-7)^2=q^2+\color{magenta}{2.q.(-7)}+(-7)^2=q^2\color{magenta}{-14q}+49\)
6. \((b-12)^2=b^2+\color{magenta}{2.b.(-12)}+(-12)^2=b^2\color{magenta}{-24b}+144\)
7. \((\color{red}{-14a}\color{blue}{-7})(\color{red}{14a}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(14a)}^2=49-196a^2\)
8. \((2q-15)^2=(2q)^2+\color{magenta}{2.(2q).(-15)}+(-15)^2=4q^2\color{magenta}{-60q}+225\)
9. \((p+10)(p+10)=(p+10)^2=p^2+\color{magenta}{2.p.10}+10^2=p^2\color{magenta}{+20p}+100\)
10. \((\color{blue}{q}\color{red}{-15})(\color{blue}{q}\color{red}{+15})=\color{blue}{q}^2-\color{red}{15}^2=q^2-225\)
11. \((\color{blue}{-11a}\color{red}{-13})(\color{blue}{-11a}\color{red}{+13})=\color{blue}{(-11a)}^2-\color{red}{(-13)}^2=121a^2-169\)
12. \((\color{blue}{s}\color{red}{+9})(\color{blue}{s}\color{red}{-9})=\color{blue}{s}^2-\color{red}{9}^2=s^2-81\)