(a² + 4b - c²)² - 16a²b³ factorise
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Answer:
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(a^{2}+4b-1c^{2})^{2}-16a^{2}b^{3}
(a2+4b−1c2)2−16a2b3
Simplify
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({\color{#c92786}{a^{2}+4b-c^{2}}})^{2}-16a^{2}b^{3}
(a2+4b−c2)2−16a2b3
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({\color{#c92786}{a^{2}-c^{2}+4b}})^{2}-16a^{2}b^{3}
(a2−c2+4b)2−16a2b3
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Expand the square
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\left(a^{2}-c^{2}+4b\right)^{2}-16a^{2}b^{3}
(a2−c2+4b)2−16a2b3
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(a^{2}-c^{2}+4b)(a^{2}-c^{2}+4b)-16a^{2}b^{3}
(a2−c2+4b)(a2−c2+4b)−16a2b3
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{\color{#c92786}{(a^{2}-c^{2}+4b)(a^{2}-c^{2}+4b)}}-16a^{2}b^{3}
(a2−c2+4b)(a2−c2+4b)−16a2b3
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{\color{#c92786}{(a^{2}-c^{2}+4b) \cdot a^{2}+(a^{2}-c^{2}+4b)\left(-c^{2}\right)+4b(a^{2}-c^{2}+4b)}}-16a^{2}b^{3}
(a2−c2+4b)⋅a2+(a2−c2+4b)(−c2)+4b(a2−c2+4b)−16a2b3
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{\color{#c92786}{(a^{2}-c^{2}+4b) \cdot a^{2}}}+(a^{2}-c^{2}+4b)\left(-c^{2}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
(a2−c2+4b)⋅a2+(a2−c2+4b)(−c2)+4b(a2−c2+4b)−16a2b3
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{\color{#c92786}{a^{4}-c^{2} \cdot a^{2}+4ba^{2}}}+(a^{2}-c^{2}+4b)\left(-c^{2}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4−c2⋅a2+4ba2+(a2−c2+4b)(−c2)+4b(a2−c2+4b)−16a2b3
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Rearrange terms
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{\color{#c92786}{a^{4}-c^{2} \cdot a^{2}+4ba^{2}}}+(a^{2}-c^{2}+4b)\left(-c^{2}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4−c2⋅a2+4ba2+(a2−c2+4b)(−c2)+4b(a2−c2+4b)−16a2b3
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{\color{#c92786}{a^{4}+4ba^{2}-c^{2} \cdot a^{2}}}+(a^{2}-c^{2}+4b)\left(-c^{2}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2+(a2−c2+4b)(−c2)+4b(a2−c2+4b)−16a2b3
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Re-order terms so that constants are on the left
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}+(a^{2}-c^{2}+4b)\left(-c^{2}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2+(a2−c2+4b)(−c2)+4b(a2−c2+4b)−16a2b3
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-(a^{2}-c^{2}+4b) \cdot c^{2}+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−(a2−c2+4b)⋅c2+4b(a2−c2+4b)−16a2b3
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Distribute
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-{\color{#c92786}{(a^{2}-c^{2}+4b) \cdot c^{2}}}+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−(a2−c2+4b)⋅c2+4b(a2−c2+4b)−16a2b3
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-\left({\color{#c92786}{a^{2}c^{2}-c^{2} \cdot c^{2}+4bc^{2}}}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−(a2c2−c2⋅c2+4bc2)+4b(a2−c2+4b)−16a2b3
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Rearrange terms
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-\left({\color{#c92786}{a^{2}c^{2}-c^{2} \cdot c^{2}+4bc^{2}}}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−(a2c2−c2⋅c2+4bc2)+4b(a2−c2+4b)−16a2b3
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-\left({\color{#c92786}{a^{2}c^{2}+4bc^{2}-c^{2} \cdot c^{2}}}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−(a2c2+4bc2−c2⋅c2)+4b(a2−c2+4b)−16a2b3
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Distribute
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-\left(a^{2}c^{2}+4bc^{2}-c^{2} \cdot c^{2}\right)+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−(a2c2+4bc2−c2⋅c2)+4b(a2−c2+4b)−16a2b3
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a^{4}+4ba^{2}-c^{2} \cdot a^{2}-1a^{2}c^{2}-4bc^{2}-1\left(-c^{2}\right) \cdot c^{2}+4b(a^{2}-c^{2}+4b)-16a^{2}b^{3}
a4+4ba2−c2⋅a2−1a2c2−4bc2−1(−c2)⋅c2+4b(a2−c2+4b)−16a2b3
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Solution
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Step-by-step explanation:
Mark my answer as brainlist answer