Question

determine the product of linear and quadratic factors. verify graphically that the expressions are equivalent.
item
$x(x^2 + 3x - 4)$
$x(x^2 + 3x - 4)=x^3 + 3x^2 - 4x$
the graph of the original expression and the graph of the final expression are the same. so the expressions are equivalent.

type the answer in the space provided. use numbers instead of words.

$7x(x + 5)^2$
$=$ \boxed{}

Explanation:

Step1: Expand quadratic factor first

First expand $(x+3)^2$ using the formula $(a+b)^2=a^2+2ab+b^2$:
$$(x+3)^2 = x^2 + 6x + 9$$

Step2: Multiply by linear factor

Multiply the result by $7x$ using distributive property:
$$7x(x^2 + 6x + 9) = 7x \cdot x^2 + 7x \cdot 6x + 7x \cdot 9$$

Step3: Simplify each term

Calculate each product and combine:
$$7x^3 + 42x^2 + 63x$$

Answer:

$7x^3 + 42x^2 + 63x$