We have seen that $(x + 3)(x + 4) = x^2 + 7x + 12$.

Also $(x + 6)(x + 7) = x^2 + 13x + 42$.

Generalise the pattern to get an expression for $(x + a)(x + b)$.                        [Page No. 80]

When two binomials are multiplied,

$$(x + a)(x + b) = x^2 + (a + b)x + ab.$$

Thus, the coefficient of $x$ is the sum of the two numbers, $a + b$ and the constant term is their product, $ab$.

For example, $(x + 3)(x + 4) = x^2 + 7x + 12$,

since $3 + 4 = 7$ and $3 \times 4 = 12$.

Similarly, $(x + 6)(x + 7) = x^2 + 13x + 42$,

since $6 + 7 = 13$ and $6 \times 7 = 42$.

More generally, $(px + a)(qx + b) = pqx^2 + (pb + qa)x + ab$.

Here, the coefficient of $x^2$ is the product of the leading coefficients, the coefficient of $x$ is the sum of the cross-products, and the constant term is the product of the constants.