Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((5y-12)(5y-12)\)
2. \((-14b^3+8y)(14b^3+8y)\)
3. \((q-6)(q+6)\)
4. \((a+3)(a-3)\)
5. \((-5b^3+12)(-5b^3-12)\)
6. \((-6y^2-10)(6y^2-10)\)
7. \((-14x+4)(14x+4)\)
8. \((-14s^3-14p)^2\)
9. \((-16a^5+12)(16a^5+12)\)
10. \((-4b^2-4x)(-4b^2+4x)\)
11. \((8s^4+8)(-8s^4+8)\)
12. \((y+1)(y-1)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((5y-12)(5y-12)=(5y-12)^2=(5y)^2+\color{magenta}{2.(5y).(-12)}+(-12)^2=25y^2\color{magenta}{-120y}+144\)
2. \((\color{red}{-14b^3}\color{blue}{+8y})(\color{red}{14b^3}\color{blue}{+8y})=\color{blue}{(8y)}^2-\color{red}{(14b^3)}^2=64y^2-196b^{6}\)
3. \((\color{blue}{q}\color{red}{-6})(\color{blue}{q}\color{red}{+6})=\color{blue}{q}^2-\color{red}{6}^2=q^2-36\)
4. \((\color{blue}{a}\color{red}{+3})(\color{blue}{a}\color{red}{-3})=\color{blue}{a}^2-\color{red}{3}^2=a^2-9\)
5. \((\color{blue}{-5b^3}\color{red}{+12})(\color{blue}{-5b^3}\color{red}{-12})=\color{blue}{(-5b^3)}^2-\color{red}{12}^2=25b^{6}-144\)
6. \((\color{red}{-6y^2}\color{blue}{-10})(\color{red}{6y^2}\color{blue}{-10})=\color{blue}{(-10)}^2-\color{red}{(6y^2)}^2=100-36y^{4}\)
7. \((\color{red}{-14x}\color{blue}{+4})(\color{red}{14x}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(14x)}^2=16-196x^2\)
8. \((-14s^3-14p)^2=(-14s^3)^2\color{magenta}{+2.(-14s^3).(-14p)}+(-14p)^2=196s^{6}\color{magenta}{+392ps^3}+196p^2\)
9. \((\color{red}{-16a^5}\color{blue}{+12})(\color{red}{16a^5}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(16a^5)}^2=144-256a^{10}\)
10. \((\color{blue}{-4b^2}\color{red}{-4x})(\color{blue}{-4b^2}\color{red}{+4x})=\color{blue}{(-4b^2)}^2-\color{red}{(-4x)}^2=16b^{4}-16x^2\)
11. \((\color{red}{8s^4}\color{blue}{+8})(\color{red}{-8s^4}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(8s^4)}^2=64-64s^{8}\)
12. \((\color{blue}{y}\color{red}{+1})(\color{blue}{y}\color{red}{-1})=\color{blue}{y}^2-\color{red}{1}^2=y^2-1\)