Question

2-92. multiply each of the following expressions.
a. $2x^2(3x + 4x^2y)$
b. $(x^3y^2)^4(x^2y)$

Explanation:

Step1: Distribute $2x^2$ to each term

$2x^2(3x) + 2x^2(4x^2y)$

Step2: Multiply coefficients and add exponents

$6x^{2+1} + 8x^{2+2}y$

Step3: Simplify exponents for part a

$6x^3 + 8x^4y$

Step4: Simplify the power of a product

$(x^{3\times4}y^{2\times4})(x^2y) = (x^{12}y^8)(x^2y)$

Step5: Multiply like terms, add exponents

$x^{12+2}y^{8+1}$

Step6: Simplify exponents for part b

$x^{14}y^9$

Answer:

a. $6x^3 + 8x^4y$
b. $x^{14}y^9$