Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((a+1)(a+1)=(a+1)^2=a^2+\color{magenta}{2.a.1}+1^2=a^2\color{magenta}{+2a}+1\)
2. \((-5b^2+3q)^2=(-5b^2)^2\color{magenta}{+2.(-5b^2).(3q)}+(3q)^2=25b^{4}\color{magenta}{-30b^2q}+9q^2\)
3. \((\color{blue}{s}\color{red}{+1})(\color{blue}{s}\color{red}{-1})=\color{blue}{s}^2-\color{red}{1}^2=s^2-1\)
4. \((15q^5+16)(15q^5+16)=(15q^5+16)^2=(15q^5)^2\color{magenta}{+2.(15q^5).16}+16^2=225q^{10}\color{magenta}{+480q^5}+256\)
5. \((\color{red}{-4y^2}\color{blue}{+5p})(\color{red}{4y^2}\color{blue}{+5p})=\color{blue}{(5p)}^2-\color{red}{(4y^2)}^2=25p^2-16y^{4}\)
6. \((\color{red}{3q^5}\color{blue}{+16b})(\color{red}{-3q^5}\color{blue}{+16b})=\color{blue}{(16b)}^2-\color{red}{(3q^5)}^2=256b^2-9q^{10}\)
7. \((\color{blue}{2q^5}\color{red}{+11})(\color{blue}{2q^5}\color{red}{-11})=\color{blue}{(2q^5)}^2-\color{red}{11}^2=4q^{10}-121\)
8. \((8y^4+6)(8y^4+6)=(8y^4+6)^2=(8y^4)^2\color{magenta}{+2.(8y^4).6}+6^2=64y^{8}\color{magenta}{+96y^4}+36\)
9. \((\color{red}{-3q}\color{blue}{-14})(\color{red}{3q}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(3q)}^2=196-9q^2\)
10. \((\color{blue}{p}\color{red}{+6})(\color{blue}{p}\color{red}{-6})=\color{blue}{p}^2-\color{red}{6}^2=p^2-36\)
11. \((\color{blue}{q}\color{red}{-7})(\color{blue}{q}\color{red}{+7})=\color{blue}{q}^2-\color{red}{7}^2=q^2-49\)
12. \((14p+11)(14p+11)=(14p+11)^2=(14p)^2+\color{magenta}{2.(14p).11}+11^2=196p^2\color{magenta}{+308p}+121\)