Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((16b+9)^2=(16b)^2+\color{magenta}{2.(16b).9}+9^2=256b^2\color{magenta}{+288b}+81\)
2. \((a+11)(a+11)=(a+11)^2=a^2+\color{magenta}{2.a.11}+11^2=a^2\color{magenta}{+22a}+121\)
3. \((\color{blue}{-14q^3}\color{red}{+y})(\color{blue}{-14q^3}\color{red}{-y})=\color{blue}{(-14q^3)}^2-\color{red}{(1y)}^2=196q^{6}-1y^2\)
4. \((3y-16)^2=(3y)^2+\color{magenta}{2.(3y).(-16)}+(-16)^2=9y^2\color{magenta}{-96y}+256\)
5. \((15x^5-8)^2=(15x^5)^2\color{magenta}{+2.(15x^5).(-8)}+(-8)^2=225x^{10}\color{magenta}{-240x^5}+64\)
6. \((\color{blue}{a}\color{red}{+5})(\color{blue}{a}\color{red}{-5})=\color{blue}{a}^2-\color{red}{5}^2=a^2-25\)
7. \((b-4)(b-4)=(b-4)^2=b^2+\color{magenta}{2.b.(-4)}+(-4)^2=b^2\color{magenta}{-8b}+16\)
8. \((7p+11)^2=(7p)^2+\color{magenta}{2.(7p).11}+11^2=49p^2\color{magenta}{+154p}+121\)
9. \((\color{blue}{3x^3}\color{red}{-2p})(\color{blue}{3x^3}\color{red}{+2p})=\color{blue}{(3x^3)}^2-\color{red}{(-2p)}^2=9x^{6}-4p^2\)
10. \((\color{blue}{p}\color{red}{+7})(\color{blue}{p}\color{red}{-7})=\color{blue}{p}^2-\color{red}{7}^2=p^2-49\)
11. \((\color{red}{14p^5}\color{blue}{-14s})(\color{red}{-14p^5}\color{blue}{-14s})=\color{blue}{(-14s)}^2-\color{red}{(14p^5)}^2=196s^2-196p^{10}\)
12. \((\color{red}{-3x^2}\color{blue}{+5a})(\color{red}{3x^2}\color{blue}{+5a})=\color{blue}{(5a)}^2-\color{red}{(3x^2)}^2=25a^2-9x^{4}\)