Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((-14b^2+15p)(-14b^2+15p)=(-14b^2+15p)^2=(-14b^2)^2\color{magenta}{+2.(-14b^2).(15p)}+(15p)^2=196b^{4}\color{magenta}{-420b^2p}+225p^2\)
2. \((\color{blue}{x^2}\color{red}{+5b})(\color{blue}{x^2}\color{red}{-5b})=\color{blue}{(x^2)}^2-\color{red}{(5b)}^2=x^{4}-25b^2\)
3. \((-11a-15)^2=(-11a)^2+\color{magenta}{2.(-11a).(-15)}+(-15)^2=121a^2\color{magenta}{+330a}+225\)
4. \((\color{blue}{11a^3}\color{red}{+8y})(\color{blue}{11a^3}\color{red}{-8y})=\color{blue}{(11a^3)}^2-\color{red}{(8y)}^2=121a^{6}-64y^2\)
5. \((\color{red}{-12x^2}\color{blue}{+4})(\color{red}{12x^2}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(12x^2)}^2=16-144x^{4}\)
6. \((\color{blue}{3x^4}\color{red}{+10a})(\color{blue}{3x^4}\color{red}{-10a})=\color{blue}{(3x^4)}^2-\color{red}{(10a)}^2=9x^{8}-100a^2\)
7. \((x^5+13)(x^5+13)=(x^5+13)^2=(x^5)^2\color{magenta}{+2.(x^5).13}+13^2=1x^{10}\color{magenta}{+26x^5}+169\)
8. \((-9p-5)^2=(-9p)^2+\color{magenta}{2.(-9p).(-5)}+(-5)^2=81p^2\color{magenta}{+90p}+25\)
9. \((\color{red}{7y}\color{blue}{-4})(\color{red}{-7y}\color{blue}{-4})=\color{blue}{(-4)}^2-\color{red}{(7y)}^2=16-49y^2\)
10. \((\color{red}{-6s^5}\color{blue}{+13q})(\color{red}{6s^5}\color{blue}{+13q})=\color{blue}{(13q)}^2-\color{red}{(6s^5)}^2=169q^2-36s^{10}\)
11. \((-2b-2)(-2b-2)=(-2b-2)^2=(-2b)^2+\color{magenta}{2.(-2b).(-2)}+(-2)^2=4b^2\color{magenta}{+8b}+4\)
12. \((x+2)^2=x^2+\color{magenta}{2.x.2}+2^2=x^2\color{magenta}{+4x}+4\)