Using the binomial theorem,
(2x–5y)7=7C0(2x)7(–5y)0+
7C1(2x)6(–5y)1+7C2(2x)5(–5y)2 +
7C3(2x)4(–5y)3+7C4(2x)3(–5y)4+
7C5(2x)2(–5y)5+7C6(2x)1(–5y)6+
7C7(2x)0(–5y)7
Then simplifying, we have,
=(1)(128x7)(1)+(7)(64x6)(–5y)+
(21)(32x5)(25y2)+(35)(16x4)(–125y3)+
(35)(8x3)(625y4)+(21)(4x2)(–3125y5)+
(7)(2x)(15625y6)+(1)(1)(–78125y7)
=128x7–2240x6y+16800x5y2–
70000x4y3+175000x3y4–
262500x2y5+218750xy6–78125y7
Therefore, the required fourth term is
70000x4y3
#AnswerForTrees
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