Question

formative focus: simplify polynomials by combining like terms

1. a large white square represents an ( x^2 )-tile, a large black square represents a ( -x^2 )-tile, a white rectangle represents an ( x )-tile, a black rectangle represents a ( -x )-tile, a small white square represents a 1-tile, and a small black square represents a -1-tile.

write the simplified polynomial.
image of tiles

1. simplify: ( 5x - 4 + 5 - 2x + 4x - 3 + 3x - 5 )
2. a) group like terms, then simplify.

( 5xy + 8x^2 - 4x - 6 + 6x^2 - 3xy + 3 )

Explanation:

Problem 2

Step1: Identify like terms

The \(x\)-terms: \(5x\), \(-2x\), \(4x\), \(3x\)
The constant terms: \(-4\), \(5\), \(-3\), \(-5\)

Step2: Combine \(x\)-terms

\(5x - 2x + 4x + 3x=(5 - 2 + 4 + 3)x = 10x\)

Step3: Combine constant terms

\(-4 + 5 - 3 - 5=(-4 - 3 - 5)+5=-12 + 5=-7\)

Step4: Combine results

The simplified polynomial is \(10x-7\)

Step1: Group like terms

\(5xy-3xy + 8x^{2}+6x^{2}-4x-6 + 3\)

Step2: Combine \(xy\)-terms

\(5xy-3xy=(5 - 3)xy = 2xy\)

Step3: Combine \(x^{2}\)-terms

\(8x^{2}+6x^{2}=(8 + 6)x^{2}=14x^{2}\)

Step4: Combine constant terms

\(-6 + 3=-3\)

Step5: Combine results

The simplified polynomial is \(14x^{2}+2xy-4x - 3\)

Answer:

\(10x - 7\)

Problem 3a