Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{10y^4}\color{red}{-4})(\color{blue}{10y^4}\color{red}{+4})=\color{blue}{(10y^4)}^2-\color{red}{(-4)}^2=100y^{8}-16\)
2. \((13a^2+12b)(13a^2+12b)=(13a^2+12b)^2=(13a^2)^2\color{magenta}{+2.(13a^2).(12b)}+(12b)^2=169a^{4}\color{magenta}{+312a^2b}+144b^2\)
3. \((\color{red}{3p^3}\color{blue}{+a})(\color{red}{-3p^3}\color{blue}{+a})=\color{blue}{(1a)}^2-\color{red}{(3p^3)}^2=1a^2-9p^{6}\)
4. \((9b^2-12)(9b^2-12)=(9b^2-12)^2=(9b^2)^2\color{magenta}{+2.(9b^2).(-12)}+(-12)^2=81b^{4}\color{magenta}{-216b^2}+144\)
5. \((p-7)(p-7)=(p-7)^2=p^2+\color{magenta}{2.p.(-7)}+(-7)^2=p^2\color{magenta}{-14p}+49\)
6. \((8p+7)^2=(8p)^2+\color{magenta}{2.(8p).7}+7^2=64p^2\color{magenta}{+112p}+49\)
7. \((\color{blue}{-2q^4}\color{red}{-7})(\color{blue}{-2q^4}\color{red}{+7})=\color{blue}{(-2q^4)}^2-\color{red}{(-7)}^2=4q^{8}-49\)
8. \((\color{blue}{-15y^4}\color{red}{-12b})(\color{blue}{-15y^4}\color{red}{+12b})=\color{blue}{(-15y^4)}^2-\color{red}{(-12b)}^2=225y^{8}-144b^2\)
9. \((\color{blue}{15y}\color{red}{-8})(\color{blue}{15y}\color{red}{+8})=\color{blue}{(15y)}^2-\color{red}{(-8)}^2=225y^2-64\)
10. \((\color{blue}{4q^2}\color{red}{+14x})(\color{blue}{4q^2}\color{red}{-14x})=\color{blue}{(4q^2)}^2-\color{red}{(14x)}^2=16q^{4}-196x^2\)
11. \((15b-14)^2=(15b)^2+\color{magenta}{2.(15b).(-14)}+(-14)^2=225b^2\color{magenta}{-420b}+196\)
12. \((13b+9)^2=(13b)^2+\color{magenta}{2.(13b).9}+9^2=169b^2\color{magenta}{+234b}+81\)