Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{q}\color{red}{+13})(\color{blue}{q}\color{red}{-13})=\color{blue}{q}^2-\color{red}{13}^2=q^2-169\)
2. \((s+13)(s+13)=(s+13)^2=s^2+\color{magenta}{2.s.13}+13^2=s^2\color{magenta}{+26s}+169\)
3. \((10s^5+3x)(10s^5+3x)=(10s^5+3x)^2=(10s^5)^2\color{magenta}{+2.(10s^5).(3x)}+(3x)^2=100s^{10}\color{magenta}{+60s^5x}+9x^2\)
4. \((-14x^5-a)^2=(-14x^5)^2\color{magenta}{+2.(-14x^5).(-a)}+(-a)^2=196x^{10}\color{magenta}{+28ax^5}+1a^2\)
5. \((\color{blue}{11a^3}\color{red}{+16})(\color{blue}{11a^3}\color{red}{-16})=\color{blue}{(11a^3)}^2-\color{red}{16}^2=121a^{6}-256\)
6. \((\color{red}{5a^3}\color{blue}{-15q})(\color{red}{-5a^3}\color{blue}{-15q})=\color{blue}{(-15q)}^2-\color{red}{(5a^3)}^2=225q^2-25a^{6}\)
7. \((\color{blue}{-4x}\color{red}{-6})(\color{blue}{-4x}\color{red}{+6})=\color{blue}{(-4x)}^2-\color{red}{(-6)}^2=16x^2-36\)
8. \((\color{red}{14y^2}\color{blue}{-15b})(\color{red}{-14y^2}\color{blue}{-15b})=\color{blue}{(-15b)}^2-\color{red}{(14y^2)}^2=225b^2-196y^{4}\)
9. \((\color{red}{7y^4}\color{blue}{+12a})(\color{red}{-7y^4}\color{blue}{+12a})=\color{blue}{(12a)}^2-\color{red}{(7y^4)}^2=144a^2-49y^{8}\)
10. \((-15y^3+7)^2=(-15y^3)^2\color{magenta}{+2.(-15y^3).7}+7^2=225y^{6}\color{magenta}{-210y^3}+49\)
11. \((\color{red}{-4x^2}\color{blue}{+5y})(\color{red}{4x^2}\color{blue}{+5y})=\color{blue}{(5y)}^2-\color{red}{(4x^2)}^2=25y^2-16x^{4}\)
12. \((\color{red}{-13p}\color{blue}{+3})(\color{red}{13p}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(13p)}^2=9-169p^2\)