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blsea [12.9K]
3 years ago
8

(4x + 4)(ax – 1) – x2 +4

Mathematics
1 answer:
Oksana_A [137]3 years ago
8 0

Answer:

b=-3

Step-by-step explanation:

If the expression simplifies to bx that means the x^{2} terms and the constant terms must be cancel out.

Simplify it first.

(4x+4)(ax-1)-x^{2} +4\\=(4ax^{2} -4x+4ax-4)-x^{2} +4\\=4ax^{2} -x^{2} -4x+4ax-4+4\\=4ax^{2} -x^{2} -4x+4ax

We know –4 + 4 will cancel out. If we simplify this expression to only an x term, then the x^{2} terms should be cancelled. Therefore, we say that 4ax^2 – x^2 = 0.

4ax^{2} -x^{2} =0\\x^{2} (4a-1)=0\\4a-1=0\\4a=1\\a=\frac{1}{4}

If we put a = ¼, then we can find the value of b:

=4(\frac{1}{4} )x^{2} -x^{2} -4x+4(\frac{1}{4} )x\\=x^{2} -x^{2} -4x+x\\ (cancel out x^{2} terms)\\

=-3x

bx=-3x\\      if the  expression is equivalent to bx

Therefore, b = –3.

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Work is attached in the image provided.

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