Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-14y^3}\color{red}{+13a})(\color{blue}{-14y^3}\color{red}{-13a})=\color{blue}{(-14y^3)}^2-\color{red}{(13a)}^2=196y^{6}-169a^2\)
2. \((-2x^5-10y)^2=(-2x^5)^2\color{magenta}{+2.(-2x^5).(-10y)}+(-10y)^2=4x^{10}\color{magenta}{+40x^5y}+100y^2\)
3. \((\color{blue}{-5a}\color{red}{+7})(\color{blue}{-5a}\color{red}{-7})=\color{blue}{(-5a)}^2-\color{red}{(7)}^2=25a^2-49\)
4. \((\color{red}{8q^4}\color{blue}{+2s})(\color{red}{-8q^4}\color{blue}{+2s})=\color{blue}{(2s)}^2-\color{red}{(8q^4)}^2=4s^2-64q^{8}\)
5. \((\color{blue}{-2b^5}\color{red}{+a})(\color{blue}{-2b^5}\color{red}{-a})=\color{blue}{(-2b^5)}^2-\color{red}{(1a)}^2=4b^{10}-1a^2\)
6. \((b-2)(b-2)=(b-2)^2=b^2+\color{magenta}{2.b.(-2)}+(-2)^2=b^2\color{magenta}{-4b}+4\)
7. \((y^5+14x)(y^5+14x)=(y^5+14x)^2=(y^5)^2\color{magenta}{+2.(y^5).(14x)}+(14x)^2=y^{10}\color{magenta}{+28xy^5}+196x^2\)
8. \((\color{red}{6s}\color{blue}{+9})(\color{red}{-6s}\color{blue}{+9})=\color{blue}{9}^2-\color{red}{(6s)}^2=81-36s^2\)
9. \((\color{red}{-11y^3}\color{blue}{-q})(\color{red}{11y^3}\color{blue}{-q})=\color{blue}{(-1q)}^2-\color{red}{(11y^3)}^2=1q^2-121y^{6}\)
10. \((\color{red}{-12y^3}\color{blue}{-3})(\color{red}{12y^3}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(12y^3)}^2=9-144y^{6}\)
11. \((\color{blue}{-9x}\color{red}{-14})(\color{blue}{-9x}\color{red}{+14})=\color{blue}{(-9x)}^2-\color{red}{(-14)}^2=81x^2-196\)
12. \((-4p^2-15)^2=(-4p^2)^2\color{magenta}{+2.(-4p^2).(-15)}+(-15)^2=16p^{4}\color{magenta}{+120p^2}+225\)