Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((5b-9)^2=(5b)^2+\color{magenta}{2.(5b).(-9)}+(-9)^2=25b^2\color{magenta}{-90b}+81\)
2. \((\color{blue}{-14a^2}\color{red}{-9q})(\color{blue}{-14a^2}\color{red}{+9q})=\color{blue}{(-14a^2)}^2-\color{red}{(-9q)}^2=196a^{4}-81q^2\)
3. \((6a^2+4)(6a^2+4)=(6a^2+4)^2=(6a^2)^2\color{magenta}{+2.(6a^2).4}+4^2=36a^{4}\color{magenta}{+48a^2}+16\)
4. \((-7q-2)(-7q-2)=(-7q-2)^2=(-7q)^2+\color{magenta}{2.(-7q).(-2)}+(-2)^2=49q^2\color{magenta}{+28q}+4\)
5. \((\color{blue}{-10a}\color{red}{-13})(\color{blue}{-10a}\color{red}{+13})=\color{blue}{(-10a)}^2-\color{red}{(-13)}^2=100a^2-169\)
6. \((\color{blue}{-3q}\color{red}{+8})(\color{blue}{-3q}\color{red}{-8})=\color{blue}{(-3q)}^2-\color{red}{(8)}^2=9q^2-64\)
7. \((\color{red}{10y^3}\color{blue}{+11s})(\color{red}{-10y^3}\color{blue}{+11s})=\color{blue}{(11s)}^2-\color{red}{(10y^3)}^2=121s^2-100y^{6}\)
8. \((6b+3)(6b+3)=(6b+3)^2=(6b)^2+\color{magenta}{2.(6b).3}+3^2=36b^2\color{magenta}{+36b}+9\)
9. \((\color{red}{-14p}\color{blue}{+10})(\color{red}{14p}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(14p)}^2=100-196p^2\)
10. \((a+7)(a+7)=(a+7)^2=a^2+\color{magenta}{2.a.7}+7^2=a^2\color{magenta}{+14a}+49\)
11. \((\color{blue}{14p}\color{red}{-1})(\color{blue}{14p}\color{red}{+1})=\color{blue}{(14p)}^2-\color{red}{(-1)}^2=196p^2-1\)
12. \((\color{red}{-b^2}\color{blue}{-8})(\color{red}{b^2}\color{blue}{-8})=\color{blue}{(-8)}^2-\color{red}{(b^2)}^2=64-b^{4}\)