Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{3p^4}\color{red}{-2y})(\color{blue}{3p^4}\color{red}{+2y})=\color{blue}{(3p^4)}^2-\color{red}{(-2y)}^2=9p^{8}-4y^2\)
2. \((-12y^4-4a)(-12y^4-4a)=(-12y^4-4a)^2=(-12y^4)^2\color{magenta}{+2.(-12y^4).(-4a)}+(-4a)^2=144y^{8}\color{magenta}{+96ay^4}+16a^2\)
3. \((14x^4-11)^2=(14x^4)^2\color{magenta}{+2.(14x^4).(-11)}+(-11)^2=196x^{8}\color{magenta}{-308x^4}+121\)
4. \((\color{blue}{-16s}\color{red}{-9})(\color{blue}{-16s}\color{red}{+9})=\color{blue}{(-16s)}^2-\color{red}{(-9)}^2=256s^2-81\)
5. \((7b^5-8s)(7b^5-8s)=(7b^5-8s)^2=(7b^5)^2\color{magenta}{+2.(7b^5).(-8s)}+(-8s)^2=49b^{10}\color{magenta}{-112b^5s}+64s^2\)
6. \((\color{red}{-14y^3}\color{blue}{-11})(\color{red}{14y^3}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(14y^3)}^2=121-196y^{6}\)
7. \((5q-7)(5q-7)=(5q-7)^2=(5q)^2+\color{magenta}{2.(5q).(-7)}+(-7)^2=25q^2\color{magenta}{-70q}+49\)
8. \((14y^2-8)^2=(14y^2)^2\color{magenta}{+2.(14y^2).(-8)}+(-8)^2=196y^{4}\color{magenta}{-224y^2}+64\)
9. \((-16q^2+11b)^2=(-16q^2)^2\color{magenta}{+2.(-16q^2).(11b)}+(11b)^2=256q^{4}\color{magenta}{-352bq^2}+121b^2\)
10. \((-11s^5-2q)(-11s^5-2q)=(-11s^5-2q)^2=(-11s^5)^2\color{magenta}{+2.(-11s^5).(-2q)}+(-2q)^2=121s^{10}\color{magenta}{+44qs^5}+4q^2\)
11. \((\color{blue}{10p^3}\color{red}{+16a})(\color{blue}{10p^3}\color{red}{-16a})=\color{blue}{(10p^3)}^2-\color{red}{(16a)}^2=100p^{6}-256a^2\)
12. \((\color{red}{5y^4}\color{blue}{-11b})(\color{red}{-5y^4}\color{blue}{-11b})=\color{blue}{(-11b)}^2-\color{red}{(5y^4)}^2=121b^2-25y^{8}\)