Question

1. competency check replace each unknown box, ■, with algebra tiles to make a true statement. explain your reasoning.

a)

Explanation:

Step1: Represent the tiles as algebraic expressions

Let the large square be \(x^{2}\), the rectangle be \(x\), and the small square be \(1\).
The left - hand side (LHS) before adding the unknown is \(2x^{2}+2x - 2\) (two large squares \(+2x\) (two rectangles) and \(- 2\) (two red small squares)). The right - hand side (RHS) is \(x^{2}+3x + 1\) (one large green square \(+3x\) (three green rectangles) and \(+1\) (one white small square)).

Step2: Let the unknown be \(A\) and set up the equation

We know that \((2x^{2}+2x - 2)+A=x^{2}+3x + 1\).
To find \(A\), we use the formula \(A=(x^{2}+3x + 1)-(2x^{2}+2x - 2)\).

Step3: Simplify the expression for \(A\)

$$
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$$

In terms of algebra tiles, \(-x^{2}\) (one red large square), \(+x\) (one green rectangle), and \(+3\) (three green small squares).

Answer:

The unknown box should be replaced with one red large square (representing \(-x^{2}\)), one green rectangle (representing \(x\)), and three green small squares (representing \(+3\)).