7.9.4 Expressions in Standard Form

Algebra 17.9.4 Expressions in Standard Form

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For each expression, write an equivalent expression in standard form. Show your reasoning.

$(2 x + 5) (x + 1)$

Compare your answer:

$2 x^{2} + 7 x + 5$ . The diagram shows that $(2 x + 5) (x + 1) = 2 x \cdot x + 2 x \cdot 1 + 5 \cdot x + 5 \cdot 1$ . Adding this together gives $2 x^{2} + 7 x + 5$ in standard form.

	$2 x$	$5$
$x$	$2 x^{2}$	$5 x$
$1$	$2 x$	$5$

$(x - 2) (x + 2)$

Compare your answer:

$x^{2} - 4$ . $(x + 2) (x - 2) = x^{2} + (- 2 x) + 2 x + (- 4) = x^{2} - 4$ .The diagram also shows that $(x + 2) (x - 2) = x^{2} - 4$ .

	$x$	$2$
$x$	$x^{2}$	$2 x$
$- 2$	$- 2 x$	$- 4$

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