smc-4694-20-Like terms

Algebraic Techniques, SM-Bank 057

State the coefficients of \(\large x\) and \(\large y\) that make the expressions below equivalent? (2 marks)

\(9x+3y-\)

\(x+\)

\(y=6x+8y\)

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\(3 , 5\)

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\(9x+3y-\)

\(x+\)

\(y=6x+8y\)

\(\text{Equating the }x\ \text{values}\longrightarrow\)	\(9x-\)		\(x=6x\)
	\(\therefore\ \)		\(=3\)

\(\text{Equating the }y\ \text{values}\longrightarrow\)	\(3y+\)		\(y=8y\)
	\(\therefore\ \)		\(=5\)

Algebraic Techniques, SM-Bank 056

Write an expression for the perimeter of the shape below. Give your answer in simplest form. (2 marks)

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\(8x+6y+10\)

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\(\text{Perimeter}\)	\(=3+3y+4x+2+3+4x+2+3y\)
	\(=4x+4x+3y+3y+3+2+3+2\)
	\(=8x+6y+10\)

Algebraic Techniques, SM-Bank 055

Write an expression for the perimeter of the rectangle below. Give your answer in simplest form. (2 marks)

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\(20x+2\)

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\(\text{Method 1}\)

\(\text{Perimeter}\)	\(=7x+1+3x+7x+1+3x\)
	\(=7x+3x+7x+3x+1+1\)
	\(=20x+2\)

\(\text{Method 2 (Advanced)}\)

\(\text{Perimeter}\)	\(=2(7x+1)+2\times 3x\)
	\(=14x+2+6x\)
	\(=20x+2\)

Algebraic Techniques, SM-Bank 054

Write an expression for the perimeter of the triangle below. Give your answer in simplest form. (2 marks)

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\(5m+n\)

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\(\text{Perimeter}\)	\(=2m+(m+2n)+(2m-n)\)
	\(=2m+m+2m+2n-n\)
	\(=5m+n\)

Algebraic Techniques, SM-Bank 053 MC

Which of the following expressions is equivalent to \(16ab\)?

\(16+a+b\)
\(4a+3b+7a+2b\)
\(5ab-20ab+ab\)
\(2ab-3ab+4ab+13ab\)

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\(D\)

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\(\text{Option D:}\)

\(2ab-3ab+4ab+13ab\)

\(=16ab\)

\(\Rightarrow D\)

Algebraic Techniques, SM-Bank 052 MC

Which of the following expressions is equivalent to \(15m-4n\)?

\(11mn\)
\(8m-5n+7m+n\)
\(5m-6n+10m-2n\)
\(9m-2n-6m-2n\)

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\(B\)

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\(\text{Option B:}\)

\(8m-5n+7m+n\)	\(=8m+7m-5n+n\)
	\(=15m-4n\)

\(\Rightarrow B\)

Algebraic Techniques, SM-Bank 051 MC

Which of the following expressions is equivalent to \(4a-3b\)?

\(7ab\)
\(2a-3b-6a\)
\(b+5a-4b-a\)
\((2a)^2-3b\)

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\(C\)

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\(\text{Option C:}\)

\(b+5a-4b-a\)	\(=5a-a+b-4b\)
	\(=4a-3b\)

\(\Rightarrow C\)

Algebraic Techniques, SM-Bank 050

Simplify the expression \(2m-6m+4m-3m\). (1 mark)

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\(-3m\)

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\(2m-6m+4m-3m\)

\(=-3m\)

Algebraic Techniques, SM-Bank 049

Simplify the expression \(5x-3y-4x-2y\) by collecting like terms. (2 marks)

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\(x-5y\)

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\(5x-3y-4x-2y\)	\(=5x-4x-3y-2y\)
	\(=x-5y\)

Algebraic Techniques, SM-Bank 048

Simplify the expression \(2mn+3m+5mn-n\) by collecting like terms. (2 marks)

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\(7mn+3m-n\)

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\(2mn+3m+5mn-n\)	\(=2mn+5mn+3m-n\)
	\(=7mn+3m-n\)

Algebraic Techniques, SM-Bank 047

Simplify the expression \(4a+3b-5a+6b\) by collecting like terms. (2 marks)

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\(-a+9b\ \text{ or }\ 9b-a\)

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\(4a+3b-5a+6b\)	\(=4a-5a+3b+6b\)
	\(=-a+9b\ \text{ or }\ 9b-a\)

Algebraic Techniques, SM-Bank 046

Simplify the expression \(3x+2x+3y+y\) by collecting like terms. (2 marks)

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\(5x+4y\)

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\(3x+2x+3y+y\)

\(=5x +4y\)

Algebraic Techniques, SM-Bank 045 MC

Which of the following is a like term to \(8m\)?

\(3m^2\)
\(8mn\)
\(2m\)
\(4+m\)

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\(C\)

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\(\text{For like terms algebraic parts are identical:}\)

\(\text{Option A:}\longrightarrow m^2\neq m\)

\(\text{Option B:}\longrightarrow mn\neq m\)

\(\text{Option C:}\longrightarrow m = m\ \checkmark\)

\(\text{Option D:}\longrightarrow 4+m\neq m\)

\(\therefore\ 8m\text{ and}\ 2m\text{ are like terms.}\)

\(\Rightarrow C\)