Expand and simplify a(5a−2b)(5a+2b)a(5a-2b)(5a+2b).

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Worked solution

1

1. Recognise and expand the product of conjugate brackets

(5a−2b)(5a+2b)=(5a)2−(2b)2=25a2−4b2(5a-2b)(5a+2b)=(5a)^2-(2b)^2=25a^2-4b^2

2. Multiply the simplified bracket by $a$ and simplify

a(25a2−4b2)=25a3−4ab2a(25a^2-4b^2)=25a^3-4ab^2

Answer

25a3−4ab225a^3-4ab^2

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