Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{10s^2}\color{blue}{+12a})(\color{red}{-10s^2}\color{blue}{+12a})=\color{blue}{(12a)}^2-\color{red}{(10s^2)}^2=144a^2-100s^{4}\)
2. \((-7y+5)^2=(-7y)^2+\color{magenta}{2.(-7y).5}+5^2=49y^2\color{magenta}{-70y}+25\)
3. \((\color{blue}{4b^4}\color{red}{-10q})(\color{blue}{4b^4}\color{red}{+10q})=\color{blue}{(4b^4)}^2-\color{red}{(-10q)}^2=16b^{8}-100q^2\)
4. \((-11s^5+10x)^2=(-11s^5)^2\color{magenta}{+2.(-11s^5).(10x)}+(10x)^2=121s^{10}\color{magenta}{-220s^5x}+100x^2\)
5. \((-5b^2+5q)^2=(-5b^2)^2\color{magenta}{+2.(-5b^2).(5q)}+(5q)^2=25b^{4}\color{magenta}{-50b^2q}+25q^2\)
6. \((10s-10)(10s-10)=(10s-10)^2=(10s)^2+\color{magenta}{2.(10s).(-10)}+(-10)^2=100s^2\color{magenta}{-200s}+100\)
7. \((\color{red}{11s}\color{blue}{+14})(\color{red}{-11s}\color{blue}{+14})=\color{blue}{14}^2-\color{red}{(11s)}^2=196-121s^2\)
8. \((q^5+7)(q^5+7)=(q^5+7)^2=(q^5)^2\color{magenta}{+2.(q^5).7}+7^2=1q^{10}\color{magenta}{+14q^5}+49\)
9. \((\color{blue}{p}\color{red}{-8})(\color{blue}{p}\color{red}{+8})=\color{blue}{p}^2-\color{red}{8}^2=p^2-64\)
10. \((12a+16)(12a+16)=(12a+16)^2=(12a)^2+\color{magenta}{2.(12a).16}+16^2=144a^2\color{magenta}{+384a}+256\)
11. \((\color{red}{3x^4}\color{blue}{+12})(\color{red}{-3x^4}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(3x^4)}^2=144-9x^{8}\)
12. \((\color{red}{-5q^4}\color{blue}{-12})(\color{red}{5q^4}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(5q^4)}^2=144-25q^{8}\)