Asked by Anonymous
How do you factor this question? I don't understand
8p^2+40pq+50q^2
8p^2+40pq+50q^2
Answers
Answered by
PsyDAG
(2p + 5q)(4p + 10q)
Answered by
Bosnian
8 p² + 40 p ∙ q + 50 q² =
2 ∙ 4 p² + 2 ∙ 20 p ∙ q + 2 ∙ 25 q² =
2 ∙ ( 4 p² + 20 p ∙ q + 25 q² ) =
2 ∙ ( 4 p² + 10 p ∙ q + 10 p ∙ q + 25 q² ) =
2 ∙ [ ( 4 p² + 10 p ∙ q ) + ( 10 p ∙ q + 25 q² ) ] =
2 ∙ [ ( 2 ∙ 2 ∙ p² + 2 ∙ 5 ∙ p ∙ q ) + ( 5 ∙ 2 p ∙ q + 5 ∙ 5 q² ) ] =
2 ∙ [ 2 p ∙ ( 2 p + 5 q ) + 5 q ∙ ( 2 p + 5 q ) ] =
2 ∙ [ ( 2 p + 5 q ) ∙ 2 p + ( 2 p + 5 q ) ∙ 5 q ] =
2 ∙ ( 2 p + 5 q ) ∙ ( 2 p + 5 q ) = 2 ∙ ( 2 p + 5 q )²
2 ∙ 4 p² + 2 ∙ 20 p ∙ q + 2 ∙ 25 q² =
2 ∙ ( 4 p² + 20 p ∙ q + 25 q² ) =
2 ∙ ( 4 p² + 10 p ∙ q + 10 p ∙ q + 25 q² ) =
2 ∙ [ ( 4 p² + 10 p ∙ q ) + ( 10 p ∙ q + 25 q² ) ] =
2 ∙ [ ( 2 ∙ 2 ∙ p² + 2 ∙ 5 ∙ p ∙ q ) + ( 5 ∙ 2 p ∙ q + 5 ∙ 5 q² ) ] =
2 ∙ [ 2 p ∙ ( 2 p + 5 q ) + 5 q ∙ ( 2 p + 5 q ) ] =
2 ∙ [ ( 2 p + 5 q ) ∙ 2 p + ( 2 p + 5 q ) ∙ 5 q ] =
2 ∙ ( 2 p + 5 q ) ∙ ( 2 p + 5 q ) = 2 ∙ ( 2 p + 5 q )²
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