Question

① find g.c.f
$5x^2 + 25x$
② foil
$(2x + 2)(5x + 3) = $

Explanation:

Problem 1: Find G.C.F of \(5x^2 + 25x\)

Step 1: Factor out numerical GCF

Find the GCF of 5 and 25. The factors of 5 are 1, 5; factors of 25 are 1, 5, 25. So GCF of 5 and 25 is 5.

Step 2: Factor out variable GCF

For \(x^2\) and \(x\), the GCF is \(x\) (since \(x^2 = x \cdot x\) and \(x = x \cdot 1\)).

Step 3: Combine numerical and variable GCF

The GCF of \(5x^2\) and \(25x\) is the product of numerical GCF (5) and variable GCF (\(x\)), so \(5x\). We can check: \(5x^2 + 25x = 5x(x + 5)\), so the GCF is \(5x\).

Step 1: Multiply First terms

First terms: \(2x\) and \(5x\). Multiply them: \(2x \cdot 5x = 10x^2\).

Step 2: Multiply Outer terms

Outer terms: \(2x\) and \(3\). Multiply them: \(2x \cdot 3 = 6x\).

Step 3: Multiply Inner terms

Inner terms: \(2\) and \(5x\). Multiply them: \(2 \cdot 5x = 10x\).

Step 4: Multiply Last terms

Last terms: \(2\) and \(3\). Multiply them: \(2 \cdot 3 = 6\).

Step 5: Combine like terms

Add the results: \(10x^2 + 6x + 10x + 6\). Combine \(6x\) and \(10x\) to get \(16x\). So the result is \(10x^2 + 16x + 6\).

Answer:

\(5x\)

Problem 2: FOIL \((2x + 2)(5x + 3)\)