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Answer :
To factor the expression
[tex]$$28x^3 - 7x,$$[/tex]
follow these steps:
1. Notice that both terms in the expression have a common factor of [tex]$7x$[/tex]. Factor out [tex]$7x$[/tex]:
[tex]$$28x^3 - 7x = 7x(4x^2 - 1).$$[/tex]
2. Next, observe that the expression inside the parentheses is a difference of squares. Recall that a difference of squares
[tex]$$a^2 - b^2$$[/tex]
factors as
[tex]$$(a - b)(a + b).$$[/tex]
3. In the expression [tex]$4x^2 - 1$[/tex], recognize that [tex]$4x^2 = (2x)^2$[/tex] and [tex]$1 = 1^2$[/tex]. Using the difference of squares formula:
[tex]$$4x^2 - 1 = (2x - 1)(2x + 1).$$[/tex]
4. Substitute this back into the expression:
[tex]$$28x^3 - 7x = 7x(2x - 1)(2x + 1).$$[/tex]
Thus, the fully factored form of the expression is:
[tex]$$7x(2x-1)(2x+1).$$[/tex]
[tex]$$28x^3 - 7x,$$[/tex]
follow these steps:
1. Notice that both terms in the expression have a common factor of [tex]$7x$[/tex]. Factor out [tex]$7x$[/tex]:
[tex]$$28x^3 - 7x = 7x(4x^2 - 1).$$[/tex]
2. Next, observe that the expression inside the parentheses is a difference of squares. Recall that a difference of squares
[tex]$$a^2 - b^2$$[/tex]
factors as
[tex]$$(a - b)(a + b).$$[/tex]
3. In the expression [tex]$4x^2 - 1$[/tex], recognize that [tex]$4x^2 = (2x)^2$[/tex] and [tex]$1 = 1^2$[/tex]. Using the difference of squares formula:
[tex]$$4x^2 - 1 = (2x - 1)(2x + 1).$$[/tex]
4. Substitute this back into the expression:
[tex]$$28x^3 - 7x = 7x(2x - 1)(2x + 1).$$[/tex]
Thus, the fully factored form of the expression is:
[tex]$$7x(2x-1)(2x+1).$$[/tex]
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