Question

lesson 2.5a sheet
like terms. simplify the expression by combining like terms.

1. 13x + 8 + 2x - 7
2. 9 + 7y - 2 - 5y
3. 7x² - 10 - 2x² + 5
4. -3y² + 5y² - 7 + 9
5. 2 + 3xy - 4xy + 6
6. 6xy - 11xy + 2xy - 4xy + 7xy
7. 3x² + 3x - 4 + 7x² - 6x + 2
8. -2x - 8 + 6x + 5 + 4x + 1

geometry. find the perimeter of the rectangle. simplify the expression.
9.
10.
11.
12.

Explanation:

Step1: Combine x - terms and constants

For \(13x + 8+2x - 7\), combine \(13x\) and \(2x\), and \(8\) and \(-7\).
\((13x + 2x)+(8 - 7)=15x + 1\)

Step2: Combine y - terms and constants for \(9 + 7y-2 - 5y\)

\((7y-5y)+(9 - 2)=2y + 7\)

Step3: Combine \(x^{2}\) - terms and constants for \(7x^{2}-10 - 2x^{2}+5\)

\((7x^{2}-2x^{2})+(-10 + 5)=5x^{2}-5\)

Step4: Combine \(y^{2}\) - terms and constants for \(-3y^{2}+5y^{2}-7 + 9\)

\((-3y^{2}+5y^{2})+(-7 + 9)=2y^{2}+2\)

Step5: Combine \(xy\) - terms and constants for \(2 + 3xy-4xy+6\)

\((3xy-4xy)+(2 + 6)=-xy + 8\)

Step6: Combine \(xy\) - terms for \(6xy-11xy + 2xy-4xy+7xy\)

\((6 - 11+2-4 + 7)xy=0xy = 0\)

Step7: Combine \(x^{2}\) - terms, \(x\) - terms and constants for \(3x^{2}+3x-4 + 7x^{2}-6x + 2\)

\((3x^{2}+7x^{2})+(3x-6x)+(-4 + 2)=10x^{2}-3x-2\)

Step8: Combine \(x\) - terms and constants for \(-2x-8 + 6x+5 + 4x+1\)

\((-2x+6x + 4x)+(-8 + 5+1)=8x-2\)

Step9: Use perimeter formula for rectangle \(P = 2(l + w)\) for rectangle with \(l=x + 3\) and \(w = 5\)

\(P=2((x + 3)+5)=2(x+8)=2x + 16\)

Step10: For rectangle with \(l = 12w+8\) and \(w = 9\)

\(P=2((12w + 8)+9)=2(12w+17)=24w+34\)

Step11: For rectangle with \(l = 4y-6\) and \(w = 3\)

\(P=2((4y-6)+3)=2(4y-3)=8y-6\)

Step12: For rectangle with \(l = 5x-2\) and \(w = 3x + 4\)

\(P=2((5x-2)+(3x + 4))=2(8x + 2)=16x+4\)

Answer:

1. \(15x + 1\)
2. \(2y + 7\)
3. \(5x^{2}-5\)
4. \(2y^{2}+2\)
5. \(-xy + 8\)
6. \(0\)
7. \(10x^{2}-3x-2\)
8. \(8x-2\)
9. \(2x + 16\)
10. \(24w+34\)
11. \(8y-6\)
12. \(16x+4\)