Question

Factorize: 2x^3b^2-4x^5b^4​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{2x^3b^2-4x^5b^4}$

$\underline{\textsf{To find:}}$

$\textsf{Factors of}\;\mathsf{2x^3b^2-4x^5b^4}$

$\underline{\textsf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{2x^3b^2-4x^5b^4}$

$\mathsf{Take\;out\;2x^3b^2\;as\;common}$

$\mathsf{=2x^3b^2(1-2x^2b^2)}$

$\mathsf{This\;can\;be\;written\;as}$

$\mathsf{=2x^3b^2(1^2-(\sqrt{2}\,xb)^2)}$

$\mathsf{Using\;the\;identity\;\boxed{\bf\,a^2-b^2=(a-b)(a+b)}}$

$\mathsf{=2x^3b^2(1-\sqrt{2}\,xb)\;(1+\sqrt{2}\,xb)}$

$\therefore\boxed{\boxed{\mathsf{2x^3b^2-4x^5b^4=2x^3b^2(1-\sqrt{2}\,xb)\;(1+\sqrt{2}\,xb)}}}$

$\underline{\textsf{Find more:}}$

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