How do you multiply #(2x + y)(x^2 -3xy + 2y^2 )#?

1 Answer
Don't Memorise
Jun 26, 2015

# =color(green)( 2x^3 - 5x^2y + xy^2 + 2y^3#

Explanation:

# color(green)((2x +y))(x^2 - 3xy +2y^2)#

  • Multiplying #color(green)(2x)# with all three terms of the second bracket:
    # = color(green)(2x) . (x^2) + color(green)(2x) . (-3xy) + color(green)(2x) . (2y^2)#

# =color(green)( 2x^3 - 6x^2y + 4xy^2# .......#(1)#

  • Multiplying #color(green)(y)# with all three terms of the second bracket:

# = color(green)(y) . (x^2) + color(green)(y) . (-3xy) + color(green)(y) . (2y^2)#

# =color(green)( x^2.y - 3xy^2 + 2y^3#........#(2)#
combining #1# and #2#

# =color(green)( 2x^3 - 5x^2y + xy^2 + 2y^3#

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