Question

each expression is written as the product of linear factors. write an equivalent expression in standard form. type your answers in the boxes. a. ((3x)^2) b. (7x cdot 7x) c. ((x + 4)(x + 4)) d. ((x + 1)^2) e. ((x - 7)^2) f. ((x + n)^2)

Explanation:

Step1: Expand the squared term

$(3x)^2 = 3x \cdot 3x = 9x^2$

Step2: Expand the product of terms

$7x \cdot 7x = 49x^2$

Step3: Use FOIL method to expand

$(x+4)(x+4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16$

Step4: Expand the squared binomial

$(x+1)^2 = x^2 + 2x + 1$

Step5: Expand the squared binomial

$(x-7)^2 = x^2 - 14x + 49$

Step6: Expand the squared binomial

$(x+n)^2 = x^2 + 2nx + n^2$

Answer:

a. $9x^2$
b. $49x^2$
c. $x^2 + 8x + 16$
d. $x^2 + 2x + 1$
e. $x^2 - 14x + 49$
f. $x^2 + 2nx + n^2$