Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{p}\color{red}{+4})(\color{blue}{p}\color{red}{-4})=\color{blue}{p}^2-\color{red}{4}^2=p^2-16\)
2. \((\color{red}{12s^5}\color{blue}{+9b})(\color{red}{-12s^5}\color{blue}{+9b})=\color{blue}{(9b)}^2-\color{red}{(12s^5)}^2=81b^2-144s^{10}\)
3. \((\color{red}{11b^4}\color{blue}{-7})(\color{red}{-11b^4}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(11b^4)}^2=49-121b^{8}\)
4. \((3q-6)^2=(3q)^2+\color{magenta}{2.(3q).(-6)}+(-6)^2=9q^2\color{magenta}{-36q}+36\)
5. \((4a+1)(4a+1)=(4a+1)^2=(4a)^2+\color{magenta}{2.(4a).1}+1^2=16a^2\color{magenta}{+8a}+1\)
6. \((-8x-16)^2=(-8x)^2+\color{magenta}{2.(-8x).(-16)}+(-16)^2=64x^2\color{magenta}{+256x}+256\)
7. \((-10b^3+11)(-10b^3+11)=(-10b^3+11)^2=(-10b^3)^2\color{magenta}{+2.(-10b^3).11}+11^2=100b^{6}\color{magenta}{-220b^3}+121\)
8. \((-13s^4+11)^2=(-13s^4)^2\color{magenta}{+2.(-13s^4).11}+11^2=169s^{8}\color{magenta}{-286s^4}+121\)
9. \((\color{blue}{-8q}\color{red}{-15})(\color{blue}{-8q}\color{red}{+15})=\color{blue}{(-8q)}^2-\color{red}{(-15)}^2=64q^2-225\)
10. \((\color{blue}{15x^2}\color{red}{-8b})(\color{blue}{15x^2}\color{red}{+8b})=\color{blue}{(15x^2)}^2-\color{red}{(-8b)}^2=225x^{4}-64b^2\)
11. \((\color{blue}{q}\color{red}{+6})(\color{blue}{q}\color{red}{-6})=\color{blue}{q}^2-\color{red}{6}^2=q^2-36\)
12. \((y+3)(y+3)=(y+3)^2=y^2+\color{magenta}{2.y.3}+3^2=y^2\color{magenta}{+6y}+9\)