Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a-15)^2=a^2+\color{magenta}{2.a.(-15)}+(-15)^2=a^2\color{magenta}{-30a}+225\)
2. \((\color{red}{-7y^4}\color{blue}{+11a})(\color{red}{7y^4}\color{blue}{+11a})=\color{blue}{(11a)}^2-\color{red}{(7y^4)}^2=121a^2-49y^{8}\)
3. \((10q+4)(10q+4)=(10q+4)^2=(10q)^2+\color{magenta}{2.(10q).4}+4^2=100q^2\color{magenta}{+80q}+16\)
4. \((\color{red}{-14x^2}\color{blue}{-13b})(\color{red}{14x^2}\color{blue}{-13b})=\color{blue}{(-13b)}^2-\color{red}{(14x^2)}^2=169b^2-196x^{4}\)
5. \((8y+3)(8y+3)=(8y+3)^2=(8y)^2+\color{magenta}{2.(8y).3}+3^2=64y^2\color{magenta}{+48y}+9\)
6. \((-10p+15)(-10p+15)=(-10p+15)^2=(-10p)^2+\color{magenta}{2.(-10p).15}+15^2=100p^2\color{magenta}{-300p}+225\)
7. \((\color{red}{10q^4}\color{blue}{+6})(\color{red}{-10q^4}\color{blue}{+6})=\color{blue}{6}^2-\color{red}{(10q^4)}^2=36-100q^{8}\)
8. \((9a^5-11q)^2=(9a^5)^2\color{magenta}{+2.(9a^5).(-11q)}+(-11q)^2=81a^{10}\color{magenta}{-198a^5q}+121q^2\)
9. \((\color{red}{-2y^5}\color{blue}{-16p})(\color{red}{2y^5}\color{blue}{-16p})=\color{blue}{(-16p)}^2-\color{red}{(2y^5)}^2=256p^2-4y^{10}\)
10. \((-8x-1)(-8x-1)=(-8x-1)^2=(-8x)^2+\color{magenta}{2.(-8x).(-1)}+(-1)^2=64x^2\color{magenta}{+16x}+1\)
11. \((\color{red}{15b^3}\color{blue}{+8})(\color{red}{-15b^3}\color{blue}{+8})=\color{blue}{8}^2-\color{red}{(15b^3)}^2=64-225b^{6}\)
12. \((\color{blue}{14p^3}\color{red}{-10q})(\color{blue}{14p^3}\color{red}{+10q})=\color{blue}{(14p^3)}^2-\color{red}{(-10q)}^2=196p^{6}-100q^2\)