Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((7s^4+7x)(7s^4+7x)\)
2. \((3x^4+6)(-3x^4+6)\)
3. \((-x^5-p)(-x^5+p)\)
4. \((11y^2-15)(-11y^2-15)\)
5. \((q-2)^2\)
6. \((15y^5-3q)(15y^5+3q)\)
7. \((5x-10)^2\)
8. \((13s^3+6y)(13s^3+6y)\)
9. \((q-4)^2\)
10. \((-4s+2)(-4s+2)\)
11. \((-9p^5-8q)(-9p^5+8q)\)
12. \((11s^5+16q)(-11s^5+16q)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((7s^4+7x)(7s^4+7x)=(7s^4+7x)^2=(7s^4)^2\color{magenta}{+2.(7s^4).(7x)}+(7x)^2=49s^{8}\color{magenta}{+98s^4x}+49x^2\)
2. \((\color{red}{3x^4}\color{blue}{+6})(\color{red}{-3x^4}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(3x^4)}^2=36-9x^{8}\)
3. \((\color{blue}{-x^5}\color{red}{-p})(\color{blue}{-x^5}\color{red}{+p})=\color{blue}{(-x^5)}^2-\color{red}{(-1p)}^2=x^{10}-1p^2\)
4. \((\color{red}{11y^2}\color{blue}{-15})(\color{red}{-11y^2}\color{blue}{-15})=\color{blue}{(-15)}^2-\color{red}{(11y^2)}^2=225-121y^{4}\)
5. \((q-2)^2=q^2+\color{magenta}{2.q.(-2)}+(-2)^2=q^2\color{magenta}{-4q}+4\)
6. \((\color{blue}{15y^5}\color{red}{-3q})(\color{blue}{15y^5}\color{red}{+3q})=\color{blue}{(15y^5)}^2-\color{red}{(-3q)}^2=225y^{10}-9q^2\)
7. \((5x-10)^2=(5x)^2+\color{magenta}{2.(5x).(-10)}+(-10)^2=25x^2\color{magenta}{-100x}+100\)
8. \((13s^3+6y)(13s^3+6y)=(13s^3+6y)^2=(13s^3)^2\color{magenta}{+2.(13s^3).(6y)}+(6y)^2=169s^{6}\color{magenta}{+156s^3y}+36y^2\)
9. \((q-4)^2=q^2+\color{magenta}{2.q.(-4)}+(-4)^2=q^2\color{magenta}{-8q}+16\)
10. \((-4s+2)(-4s+2)=(-4s+2)^2=(-4s)^2+\color{magenta}{2.(-4s).2}+2^2=16s^2\color{magenta}{-16s}+4\)
11. \((\color{blue}{-9p^5}\color{red}{-8q})(\color{blue}{-9p^5}\color{red}{+8q})=\color{blue}{(-9p^5)}^2-\color{red}{(-8q)}^2=81p^{10}-64q^2\)
12. \((\color{red}{11s^5}\color{blue}{+16q})(\color{red}{-11s^5}\color{blue}{+16q})=\color{blue}{(16q)}^2-\color{red}{(11s^5)}^2=256q^2-121s^{10}\)