# 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

Relevance

(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..
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