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## Sagot :

### Step 1: Recognize the expression

We start with the given expression:

[tex]\[ (a + b)(b - a) \][/tex]

### Step 2: Apply the distributive property

The distributive property states that [tex]\( (x + y)(z + w) = xz + xw + yz + yw \)[/tex]. Applying this to our expression, we get:

[tex]\[ (a + b)(b - a) = a \cdot b + a \cdot (-a) + b \cdot b + b \cdot (-a) \][/tex]

### Step 3: Perform individual multiplications

Now, let's multiply each term:

[tex]\[ a \cdot b = ab \][/tex]

[tex]\[ a \cdot (-a) = -a^2 \][/tex]

[tex]\[ b \cdot b = b^2 \][/tex]

[tex]\[ b \cdot (-a) = -ab \][/tex]

### Step 4: Combine the products

Now, let's combine all the products:

[tex]\[ ab - a^2 + b^2 - ab \][/tex]

### Step 5: Simplify the expression

Notice that we have [tex]\(ab\)[/tex] and [tex]\(-ab\)[/tex] in the expression. They cancel each other out:

[tex]\[ (ab - ab) - a^2 + b^2 = 0 - a^2 + b^2 \][/tex]

### Step 6: Write the final simplified expression

After canceling out [tex]\(ab - ab\)[/tex], we are left with:

[tex]\[ -a^2 + b^2 \][/tex]

### Final Result

Thus, the expression [tex]\((a+b)(b-a)\)[/tex] simplifies to:

[tex]\[ -a^2 + b^2 \][/tex]