What are the coefficient of (x) and the constant term in ( (x-8)(x+2) )?

- (6) और - (16) / सही जोड़ा

For a product of two binomials, the coefficient of x is obtained by adding the two cross-products, while the constant term is obtained by multiplying the two constant terms. Here the cross-products are 2x and 8x, so their sum is 6x. The constants are 8 and 2, whose product is 16. Thus the coefficient of x is 6 and the constant term is 16, exactly as shown in option B.

Expanding verifies this carefully: \\( (x-8)(x+2)=x^2+2x-8x-16=x^2-6x-16 \\). The coefficient is read from the term 6x, and the final number is 16. Option A has the wrong sign for the coefficient, while C uses an incorrect sum and constant sign. Option D gives the wrong magnitude for the coefficient. Checking signs separately is especially important when one constant is negative.

This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.