Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((y+4)(y+4)=(y+4)^2=y^2+\color{magenta}{2.y.4}+4^2=y^2\color{magenta}{+8y}+16\)
2. \((\color{red}{-12p^5}\color{blue}{-10y})(\color{red}{12p^5}\color{blue}{-10y})=\color{blue}{(-10y)}^2-\color{red}{(12p^5)}^2=100y^2-144p^{10}\)
3. \((\color{red}{3s^5}\color{blue}{-q})(\color{red}{-3s^5}\color{blue}{-q})=\color{blue}{(-1q)}^2-\color{red}{(3s^5)}^2=1q^2-9s^{10}\)
4. \((16q^4+8)(16q^4+8)=(16q^4+8)^2=(16q^4)^2\color{magenta}{+2.(16q^4).8}+8^2=256q^{8}\color{magenta}{+256q^4}+64\)
5. \((\color{red}{10s^4}\color{blue}{+12a})(\color{red}{-10s^4}\color{blue}{+12a})=\color{blue}{(12a)}^2-\color{red}{(10s^4)}^2=144a^2-100s^{8}\)
6. \((s+5)^2=s^2+\color{magenta}{2.s.5}+5^2=s^2\color{magenta}{+10s}+25\)
7. \((\color{red}{13p^3}\color{blue}{+12})(\color{red}{-13p^3}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(13p^3)}^2=144-169p^{6}\)
8. \((-3s^5+9p)^2=(-3s^5)^2\color{magenta}{+2.(-3s^5).(9p)}+(9p)^2=9s^{10}\color{magenta}{-54ps^5}+81p^2\)
9. \((\color{red}{12b^5}\color{blue}{-13})(\color{red}{-12b^5}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(12b^5)}^2=169-144b^{10}\)
10. \((-11x^3+3)^2=(-11x^3)^2\color{magenta}{+2.(-11x^3).3}+3^2=121x^{6}\color{magenta}{-66x^3}+9\)
11. \((\color{red}{-4q^2}\color{blue}{-6s})(\color{red}{4q^2}\color{blue}{-6s})=\color{blue}{(-6s)}^2-\color{red}{(4q^2)}^2=36s^2-16q^{4}\)
12. \((\color{blue}{-12a}\color{red}{+7})(\color{blue}{-12a}\color{red}{-7})=\color{blue}{(-12a)}^2-\color{red}{(7)}^2=144a^2-49\)