Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{2y}\color{red}{+15})(\color{blue}{2y}\color{red}{-15})=\color{blue}{(2y)}^2-\color{red}{(15)}^2=4y^2-225\)
2. \((\color{blue}{14q^2}\color{red}{+12a})(\color{blue}{14q^2}\color{red}{-12a})=\color{blue}{(14q^2)}^2-\color{red}{(12a)}^2=196q^{4}-144a^2\)
3. \((\color{red}{-16q}\color{blue}{-7})(\color{red}{16q}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(16q)}^2=49-256q^2\)
4. \((\color{red}{12y^4}\color{blue}{+8s})(\color{red}{-12y^4}\color{blue}{+8s})=\color{blue}{(8s)}^2-\color{red}{(12y^4)}^2=64s^2-144y^{8}\)
5. \((10x^5-s)(10x^5-s)=(10x^5-s)^2=(10x^5)^2\color{magenta}{+2.(10x^5).(-s)}+(-s)^2=100x^{10}\color{magenta}{-20sx^5}+1s^2\)
6. \((\color{red}{-8s^2}\color{blue}{+10})(\color{red}{8s^2}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(8s^2)}^2=100-64s^{4}\)
7. \((\color{blue}{-s^4}\color{red}{-10})(\color{blue}{-s^4}\color{red}{+10})=\color{blue}{(-s^4)}^2-\color{red}{(-10)}^2=s^{8}-100\)
8. \((\color{blue}{-b}\color{red}{-9})(\color{blue}{-b}\color{red}{+9})=\color{blue}{(-b)}^2-\color{red}{(-9)}^2=b^2-81\)
9. \((4y-6)(4y-6)=(4y-6)^2=(4y)^2+\color{magenta}{2.(4y).(-6)}+(-6)^2=16y^2\color{magenta}{-48y}+36\)
10. \((11q^5+3)^2=(11q^5)^2\color{magenta}{+2.(11q^5).3}+3^2=121q^{10}\color{magenta}{+66q^5}+9\)
11. \((9b^4-5)^2=(9b^4)^2\color{magenta}{+2.(9b^4).(-5)}+(-5)^2=81b^{8}\color{magenta}{-90b^4}+25\)
12. \((\color{red}{x}\color{blue}{-2})(\color{red}{-x}\color{blue}{-2})=\color{blue}{(-2)}^2-\color{red}{(x)}^2=4-x^2\)