Question6. Simplify: $(2 x-1)(x+4)$

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $(2x - 1)(x + 4)$ .
2. We need to simplify the expression by expanding it.
3. We will use the distributive property (also known as the FOIL method for binomials) to expand the expression.

STEP 2

Apply the distributive property to expand the expression $(2x - 1)(x + 4)$ . This involves multiplying each term in the first binomial by each term in the second binomial.

STEP 3

Multiply the first terms of each binomial: $2x \times x$ .
$2x \times x = 2x^2$

STEP 4

Multiply the outer terms of the binomials: $2x \times 4$ .
$2x \times 4 = 8x$

STEP 5

Multiply the inner terms of the binomials: $-1 \times x$ .
$-1 \times x = -x$

STEP 6

Multiply the last terms of each binomial: $-1 \times 4$ .
$-1 \times 4 = -4$

STEP 7

Combine all the products obtained from the previous steps to form a single expression.
$2x^2 + 8x - x - 4$

STEP 8

Combine like terms in the expression. The like terms here are $8x$ and $-x$ .
$8x - x = 7x$

STEP 9

Write the simplified expression by combining the results.
$2x^2 + 7x - 4$
The simplified expression is $2x^2 + 7x - 4$ .

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