Sure, let's break down the expression and simplify it step-by-step.
The expression given is:
[tex]\[ 1 - 2(a - b) - 15(a - b)^2 \][/tex]
Step 1: Expand the expression [tex]\( (a - b)^2 \)[/tex]
[tex]\[ (a - b)^2 = a^2 - 2ab + b^2 \][/tex]
Step 2: Substitute [tex]\( (a - b)^2 \)[/tex] back into the expression
[tex]\[ 1 - 2(a - b) - 15(a^2 - 2ab + b^2) \][/tex]
Step 3: Distribute the [tex]\(-2\)[/tex] through the [tex]\((a - b)\)[/tex] term
[tex]\[ 1 - 2a + 2b - 15(a^2 - 2ab + b^2) \][/tex]
Step 4: Distribute [tex]\(-15\)[/tex] through the [tex]\((a^2 - 2ab + b^2)\)[/tex] term
[tex]\[ 1 - 2a + 2b - 15a^2 + 30ab - 15b^2 \][/tex]
Step 5: Combine all the terms
[tex]\[ 1 - 2a + 2b - 15a^2 + 30ab - 15b^2 \][/tex]
Thus, the expanded and simplified form of the expression [tex]\( 1 - 2(a - b) - 15(a - b)^2 \)[/tex] is:
[tex]\[ -15a^2 + 30ab - 2a - 15b^2 + 2b + 1 \][/tex]
