Answer :
Certainly! To simplify the expression [tex]\((1 - 8xy) \cdot (1 + 8xy)\)[/tex], we can use the difference of squares identity. The difference of squares identity states:
[tex]\[ (a - b)(a + b) = a^2 - b^2 \][/tex]
Here, we identify [tex]\(a = 1\)[/tex] and [tex]\(b = 8xy\)[/tex]. Applying the difference of squares formula to our expression:
[tex]\[ (1 - 8xy)(1 + 8xy) = 1^2 - (8xy)^2 \][/tex]
Now, carry out the squaring for each term:
[tex]\[ 1^2 = 1 \][/tex]
[tex]\[ (8xy)^2 = (8xy) \cdot (8xy) = 64x^2y^2 \][/tex]
Subtract these two results:
[tex]\[ 1 - 64x^2y^2 \][/tex]
Thus, the simplified form of [tex]\((1 - 8xy) \cdot (1 + 8xy)\)[/tex] is:
[tex]\[ 1 - 64x^2y^2 \][/tex]
So, we have:
[tex]\[ (1 - 8xy)(1 + 8xy) = 1 - 64x^2y^2 \][/tex]
[tex]\[ (a - b)(a + b) = a^2 - b^2 \][/tex]
Here, we identify [tex]\(a = 1\)[/tex] and [tex]\(b = 8xy\)[/tex]. Applying the difference of squares formula to our expression:
[tex]\[ (1 - 8xy)(1 + 8xy) = 1^2 - (8xy)^2 \][/tex]
Now, carry out the squaring for each term:
[tex]\[ 1^2 = 1 \][/tex]
[tex]\[ (8xy)^2 = (8xy) \cdot (8xy) = 64x^2y^2 \][/tex]
Subtract these two results:
[tex]\[ 1 - 64x^2y^2 \][/tex]
Thus, the simplified form of [tex]\((1 - 8xy) \cdot (1 + 8xy)\)[/tex] is:
[tex]\[ 1 - 64x^2y^2 \][/tex]
So, we have:
[tex]\[ (1 - 8xy)(1 + 8xy) = 1 - 64x^2y^2 \][/tex]
