Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-2x^5}\color{blue}{+14b})(\color{red}{2x^5}\color{blue}{+14b})=\color{blue}{(14b)}^2-\color{red}{(2x^5)}^2=196b^2-4x^{10}\)
2. \((-5q^4-12)(-5q^4-12)=(-5q^4-12)^2=(-5q^4)^2\color{magenta}{+2.(-5q^4).(-12)}+(-12)^2=25q^{8}\color{magenta}{+120q^4}+144\)
3. \((\color{blue}{-6x^3}\color{red}{-8})(\color{blue}{-6x^3}\color{red}{+8})=\color{blue}{(-6x^3)}^2-\color{red}{(-8)}^2=36x^{6}-64\)
4. \((15s^2-15p)^2=(15s^2)^2\color{magenta}{+2.(15s^2).(-15p)}+(-15p)^2=225s^{4}\color{magenta}{-450ps^2}+225p^2\)
5. \((3q^3-12)^2=(3q^3)^2\color{magenta}{+2.(3q^3).(-12)}+(-12)^2=9q^{6}\color{magenta}{-72q^3}+144\)
6. \((\color{blue}{y^4}\color{red}{-8b})(\color{blue}{y^4}\color{red}{+8b})=\color{blue}{(y^4)}^2-\color{red}{(-8b)}^2=y^{8}-64b^2\)
7. \((3y-3)(3y-3)=(3y-3)^2=(3y)^2+\color{magenta}{2.(3y).(-3)}+(-3)^2=9y^2\color{magenta}{-18y}+9\)
8. \((a+12)^2=a^2+\color{magenta}{2.a.12}+12^2=a^2\color{magenta}{+24a}+144\)
9. \((\color{blue}{-10a^3}\color{red}{+2b})(\color{blue}{-10a^3}\color{red}{-2b})=\color{blue}{(-10a^3)}^2-\color{red}{(2b)}^2=100a^{6}-4b^2\)
10. \((\color{blue}{-10x}\color{red}{+12})(\color{blue}{-10x}\color{red}{-12})=\color{blue}{(-10x)}^2-\color{red}{(12)}^2=100x^2-144\)
11. \((\color{blue}{s}\color{red}{-9})(\color{blue}{s}\color{red}{+9})=\color{blue}{s}^2-\color{red}{9}^2=s^2-81\)
12. \((\color{blue}{x}\color{red}{-12})(\color{blue}{x}\color{red}{+12})=\color{blue}{x}^2-\color{red}{12}^2=x^2-144\)