Factorise completely the following algebraic expressions. a. 12x² – 8xy b. x² + 8x + 15 c. 2x² + 7x + 3 d. ac + ad + bc + bd

The GCF of 12 and 8 is 4.

The terms are $x^2$ and $xy$. The common variable factor is $x$.

The overall GCF is $4x$.

The final answer is $\boxed{4x(3x - 2y)}$.

We are looking for two numbers, let's call them $p$ and $q$, such that $p \times q = 15$ and $p + q = 8$.

• $1 \times 15 = 15$, and $1 + 15 = 16$ (not 8)
• $3 \times 5 = 15$, and $3 + 5 = 8$ (this is correct) The two numbers are 3 and 5.

The final answer is $\boxed{(x + 3)(x + 5)}$.

We are looking for two numbers, $p$ and $q$, such that $p \times q = 6$ and $p + q = 7$.

• $1 \times 6 = 6$, and $1 + 6 = 7$ (this is correct) The two numbers are 1 and 6.

Factor out the GCF from each group:

The final answer is $\boxed{(2x + 1)(x + 3)}$.

From the first pair $(ac + ad)$, the GCF is $a$.

From the second pair $(bc + bd)$, the GCF is $b$.

The final answer is $\boxed{(a + b)(c + d)}$.