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Answer :
Sure! Let's factor the given expression step-by-step:
The expression we need to factor is:
[tex]\[ 9x^4 - 64y^2 \][/tex]
1. Identify the form:
This expression is a difference of squares, which generally has the form:
[tex]\[ a^2 - b^2 \][/tex]
2. Rewrite the expression in terms of squares:
Here, [tex]\( 9x^4 \)[/tex] can be written as [tex]\( (3x^2)^2 \)[/tex] and [tex]\( 64y^2 \)[/tex] can be written as [tex]\( (8y)^2 \)[/tex].
So, the expression becomes:
[tex]\[ (3x^2)^2 - (8y)^2 \][/tex]
3. Apply the difference of squares formula:
The difference of squares formula is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In our case, [tex]\( a = 3x^2 \)[/tex] and [tex]\( b = 8y \)[/tex]. Using the formula, we get:
[tex]\[ (3x^2 - 8y)(3x^2 + 8y) \][/tex]
Thus, the factored form of [tex]\( 9x^4 - 64y^2 \)[/tex] is:
[tex]\[ (3x^2 - 8y)(3x^2 + 8y) \][/tex]
So the answer is:
[tex]\[
(3x^2 - 8y)(3x^2 + 8y)
\][/tex]
The expression we need to factor is:
[tex]\[ 9x^4 - 64y^2 \][/tex]
1. Identify the form:
This expression is a difference of squares, which generally has the form:
[tex]\[ a^2 - b^2 \][/tex]
2. Rewrite the expression in terms of squares:
Here, [tex]\( 9x^4 \)[/tex] can be written as [tex]\( (3x^2)^2 \)[/tex] and [tex]\( 64y^2 \)[/tex] can be written as [tex]\( (8y)^2 \)[/tex].
So, the expression becomes:
[tex]\[ (3x^2)^2 - (8y)^2 \][/tex]
3. Apply the difference of squares formula:
The difference of squares formula is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In our case, [tex]\( a = 3x^2 \)[/tex] and [tex]\( b = 8y \)[/tex]. Using the formula, we get:
[tex]\[ (3x^2 - 8y)(3x^2 + 8y) \][/tex]
Thus, the factored form of [tex]\( 9x^4 - 64y^2 \)[/tex] is:
[tex]\[ (3x^2 - 8y)(3x^2 + 8y) \][/tex]
So the answer is:
[tex]\[
(3x^2 - 8y)(3x^2 + 8y)
\][/tex]
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