Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((8y^2-3)(-8y^2-3)\)
2. \((a+2)(a+2)\)
3. \((-15q^3-9s)(-15q^3+9s)\)
4. \((-3q^4+9a)(-3q^4+9a)\)
5. \((5a-7)(5a-7)\)
6. \((12y^4-5q)(12y^4-5q)\)
7. \((-13y+16)^2\)
8. \((-8q^2-12x)(8q^2-12x)\)
9. \((-12s-14)(-12s-14)\)
10. \((6x^3+12)(6x^3-12)\)
11. \((14p+3)^2\)
12. \((16a^3-15b)(16a^3+15b)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{8y^2}\color{blue}{-3})(\color{red}{-8y^2}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(8y^2)}^2=9-64y^{4}\)
2. \((a+2)(a+2)=(a+2)^2=a^2+\color{magenta}{2.a.2}+2^2=a^2\color{magenta}{+4a}+4\)
3. \((\color{blue}{-15q^3}\color{red}{-9s})(\color{blue}{-15q^3}\color{red}{+9s})=\color{blue}{(-15q^3)}^2-\color{red}{(-9s)}^2=225q^{6}-81s^2\)
4. \((-3q^4+9a)(-3q^4+9a)=(-3q^4+9a)^2=(-3q^4)^2\color{magenta}{+2.(-3q^4).(9a)}+(9a)^2=9q^{8}\color{magenta}{-54aq^4}+81a^2\)
5. \((5a-7)(5a-7)=(5a-7)^2=(5a)^2+\color{magenta}{2.(5a).(-7)}+(-7)^2=25a^2\color{magenta}{-70a}+49\)
6. \((12y^4-5q)(12y^4-5q)=(12y^4-5q)^2=(12y^4)^2\color{magenta}{+2.(12y^4).(-5q)}+(-5q)^2=144y^{8}\color{magenta}{-120qy^4}+25q^2\)
7. \((-13y+16)^2=(-13y)^2+\color{magenta}{2.(-13y).16}+16^2=169y^2\color{magenta}{-416y}+256\)
8. \((\color{red}{-8q^2}\color{blue}{-12x})(\color{red}{8q^2}\color{blue}{-12x})=\color{blue}{(-12x)}^2-\color{red}{(8q^2)}^2=144x^2-64q^{4}\)
9. \((-12s-14)(-12s-14)=(-12s-14)^2=(-12s)^2+\color{magenta}{2.(-12s).(-14)}+(-14)^2=144s^2\color{magenta}{+336s}+196\)
10. \((\color{blue}{6x^3}\color{red}{+12})(\color{blue}{6x^3}\color{red}{-12})=\color{blue}{(6x^3)}^2-\color{red}{12}^2=36x^{6}-144\)
11. \((14p+3)^2=(14p)^2+\color{magenta}{2.(14p).3}+3^2=196p^2\color{magenta}{+84p}+9\)
12. \((\color{blue}{16a^3}\color{red}{-15b})(\color{blue}{16a^3}\color{red}{+15b})=\color{blue}{(16a^3)}^2-\color{red}{(-15b)}^2=256a^{6}-225b^2\)