Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15y^2+2)^2=(15y^2)^2\color{magenta}{+2.(15y^2).2}+2^2=225y^{4}\color{magenta}{+60y^2}+4\)
2. \((\color{red}{4b}\color{blue}{-9})(\color{red}{-4b}\color{blue}{-9})=\color{blue}{(-9)}^2-\color{red}{(4b)}^2=81-16b^2\)
3. \((-14y^5-6s)^2=(-14y^5)^2\color{magenta}{+2.(-14y^5).(-6s)}+(-6s)^2=196y^{10}\color{magenta}{+168sy^5}+36s^2\)
4. \((\color{blue}{a}\color{red}{-14})(\color{blue}{a}\color{red}{+14})=\color{blue}{a}^2-\color{red}{14}^2=a^2-196\)
5. \((\color{blue}{s}\color{red}{+1})(\color{blue}{s}\color{red}{-1})=\color{blue}{s}^2-\color{red}{1}^2=s^2-1\)
6. \((\color{blue}{15q^2}\color{red}{-13x})(\color{blue}{15q^2}\color{red}{+13x})=\color{blue}{(15q^2)}^2-\color{red}{(-13x)}^2=225q^{4}-169x^2\)
7. \((x-9)^2=x^2+\color{magenta}{2.x.(-9)}+(-9)^2=x^2\color{magenta}{-18x}+81\)
8. \((-5p^5-15)^2=(-5p^5)^2\color{magenta}{+2.(-5p^5).(-15)}+(-15)^2=25p^{10}\color{magenta}{+150p^5}+225\)
9. \((y-8)^2=y^2+\color{magenta}{2.y.(-8)}+(-8)^2=y^2\color{magenta}{-16y}+64\)
10. \((\color{blue}{-2x^4}\color{red}{+11a})(\color{blue}{-2x^4}\color{red}{-11a})=\color{blue}{(-2x^4)}^2-\color{red}{(11a)}^2=4x^{8}-121a^2\)
11. \((\color{blue}{12b}\color{red}{+4})(\color{blue}{12b}\color{red}{-4})=\color{blue}{(12b)}^2-\color{red}{(4)}^2=144b^2-16\)
12. \((\color{blue}{s}\color{red}{-15})(\color{blue}{s}\color{red}{+15})=\color{blue}{s}^2-\color{red}{15}^2=s^2-225\)