Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((p+14)(p+14)=(p+14)^2=p^2+\color{magenta}{2.p.14}+14^2=p^2\color{magenta}{+28p}+196\)
2. \((\color{blue}{14s^2}\color{red}{-11})(\color{blue}{14s^2}\color{red}{+11})=\color{blue}{(14s^2)}^2-\color{red}{(-11)}^2=196s^{4}-121\)
3. \((\color{red}{7b}\color{blue}{-16})(\color{red}{-7b}\color{blue}{-16})=\color{blue}{(-16)}^2-\color{red}{(7b)}^2=256-49b^2\)
4. \((\color{blue}{q}\color{red}{-1})(\color{blue}{q}\color{red}{+1})=\color{blue}{q}^2-\color{red}{1}^2=q^2-1\)
5. \((-15s^5+3)^2=(-15s^5)^2\color{magenta}{+2.(-15s^5).3}+3^2=225s^{10}\color{magenta}{-90s^5}+9\)
6. \((\color{red}{-13p^2}\color{blue}{-15y})(\color{red}{13p^2}\color{blue}{-15y})=\color{blue}{(-15y)}^2-\color{red}{(13p^2)}^2=225y^2-169p^{4}\)
7. \((\color{blue}{-15y^4}\color{red}{+x})(\color{blue}{-15y^4}\color{red}{-x})=\color{blue}{(-15y^4)}^2-\color{red}{(1x)}^2=225y^{8}-1x^2\)
8. \((14q^2-10)^2=(14q^2)^2\color{magenta}{+2.(14q^2).(-10)}+(-10)^2=196q^{4}\color{magenta}{-280q^2}+100\)
9. \((s+13)(s+13)=(s+13)^2=s^2+\color{magenta}{2.s.13}+13^2=s^2\color{magenta}{+26s}+169\)
10. \((\color{blue}{-8p^4}\color{red}{-16})(\color{blue}{-8p^4}\color{red}{+16})=\color{blue}{(-8p^4)}^2-\color{red}{(-16)}^2=64p^{8}-256\)
11. \((10p+4)^2=(10p)^2+\color{magenta}{2.(10p).4}+4^2=100p^2\color{magenta}{+80p}+16\)
12. \((\color{red}{8x^3}\color{blue}{-7b})(\color{red}{-8x^3}\color{blue}{-7b})=\color{blue}{(-7b)}^2-\color{red}{(8x^3)}^2=49b^2-64x^{6}\)