Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((2x-1)^2=(2x)^2+\color{magenta}{2.(2x).(-1)}+(-1)^2=4x^2\color{magenta}{-4x}+1\)
2. \((y-13)^2=y^2+\color{magenta}{2.y.(-13)}+(-13)^2=y^2\color{magenta}{-26y}+169\)
3. \((\color{blue}{-12q^5}\color{red}{-15})(\color{blue}{-12q^5}\color{red}{+15})=\color{blue}{(-12q^5)}^2-\color{red}{(-15)}^2=144q^{10}-225\)
4. \((\color{red}{a}\color{blue}{+3})(\color{red}{-a}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(a)}^2=9-a^2\)
5. \((-10y^3+14)(-10y^3+14)=(-10y^3+14)^2=(-10y^3)^2\color{magenta}{+2.(-10y^3).14}+14^2=100y^{6}\color{magenta}{-280y^3}+196\)
6. \((\color{red}{3a}\color{blue}{+14})(\color{red}{-3a}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(3a)}^2=196-9a^2\)
7. \((10q^2+12)^2=(10q^2)^2\color{magenta}{+2.(10q^2).12}+12^2=100q^{4}\color{magenta}{+240q^2}+144\)
8. \((\color{blue}{6a^3}\color{red}{-9})(\color{blue}{6a^3}\color{red}{+9})=\color{blue}{(6a^3)}^2-\color{red}{(-9)}^2=36a^{6}-81\)
9. \((-2b-1)(-2b-1)=(-2b-1)^2=(-2b)^2+\color{magenta}{2.(-2b).(-1)}+(-1)^2=4b^2\color{magenta}{+4b}+1\)
10. \((-4q^5-4)^2=(-4q^5)^2\color{magenta}{+2.(-4q^5).(-4)}+(-4)^2=16q^{10}\color{magenta}{+32q^5}+16\)
11. \((\color{blue}{3q}\color{red}{+12})(\color{blue}{3q}\color{red}{-12})=\color{blue}{(3q)}^2-\color{red}{(12)}^2=9q^2-144\)
12. \((\color{blue}{4q^3}\color{red}{+2})(\color{blue}{4q^3}\color{red}{-2})=\color{blue}{(4q^3)}^2-\color{red}{2}^2=16q^{6}-4\)