Simplify the following problems...?

(2x^4)(5x^3)

(4x^7)(2x^4) - (6x^6)(5x^5)

(x+2)(x-3)

(3x-2)(2x+3)

4t(2t^2-t-5)

2x^2y(2x^2-3xy+y^2)

(-4c^3)^3

(4x^2y)^2(-3xy^2)^3

2 Answers

Relevance
  • Favourite answer

    (2x^4)(5x^3)

    = 2*x^4 * 5*x^3

    => Collect like terms, i.e.

    2*5 * x^4*x^3 - [This occurs as a result of grouping the integers and algebraic indices.]

    = 10 * x^(4+3) - [x^(4+3) occured this way in relation to one of the rules of indices, which states that a² * a = a^(2+1)]

    = 10 * x^7

    = 10x^7...Ans

    (4x^7)(2x^4) - (6x^6)(5x^5)

    => Collect like terms, i.e.

    = (4*2 * x^7*x^4) - (6*5 * x^6*x^5)

    = [8 * x^(7+4)] - [30 * x^(6+5)]

    = 8 * x^11 - 30 * x^11

    = 8x^11 - 30x^11

    => In the expression above, x^11 is common, then

    (8-30)x^11

    = -22 * x^11

    = -22x^11...Ans

    (x+2)(x-3)

    => Expand the expression above by multiplying (x+2) by x & -3, i.e.

    x(x+2)-3(x+2)

    = x²+2x-3x-6

    = x²-x-6...Ans

    (3x-2)(2x+3)

    => Expand the expression above by multiplying (2x+3) by 3x & -2, i.e.

    3x(2x+3)-2(2x+3)

    = 6x²+9x-4x-6

    = 6x²+5x-6...Ans

    4t(2t^2-t-5)

    => Remove the bracket, i.e.

    4t*2t^2 - 4t*t - 4t*5

    = 8t^3-4t^2-20t...Ans

    2x^2y(2x^2-3xy+y^2)

    => Remove the bracket, i.e.

    2x^2y*2x^2 - 2x^2y*3xy + 2x^2y*y^2

    = 4x^(2y+2) - 6x^(2y+1) y + 2x^(2y) y^2...Ans

    (-4c^3)^3

    = (-4)^3 * (c^3)^3

    = -64 * c^(3+3)

    = -64 * c^9

    = -64c^9...Ans

    (4x^2y)^2(-3xy^2)^3

    = (4)^2*(x^2y)^2 * (-3)^3*(x)^3(y^2)^3

    = 16x^4y * -27x^3y^6

    Collect like terms, i.e.

    = (16*-27) * (x^4y*x^3) * y^6

    = -432 * x^(4y+3) * y^6

    = -432x^(4y+3) y^6...Ans

    Source(s): Method of Calculation was sourced from New General Mathematics Series..
  • Al
    Lv 7
    7 years ago

    Go here and learn how to use F.O.I.L.

    http://www.freemathhelp.com/using-foil.html

Still have questions? Get answers by asking now.