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Margarita [4]
3 years ago
7

Factorise (2t-7)²-(5t-4)² with working pls​

Mathematics
1 answer:
sertanlavr [38]3 years ago
5 0

Answer:

33+12t−21t^2

Step-by-step explanation:

(2t-7)²-(5t-4)²

Use binomial theorem (a−b)^2 = a^2−2ab+b^2 to expand (2t-7)².

4t^2−28t+49−(5t-4)²

Use binomial theorem (a−b)^2 = a^2−2ab+b^2 to expand (5t-4)².

4t^2−28t+49−(25t^2−40t+16)

To find the opposite of 25t^2

−40t+16, find the opposite of each term.

4t^2−28t+49−25t^2−40t+16

Combine 4t^2  and −25t^2  to get −21t^2.

−21t^2−28t+49+40t−16

Combine −28t and 40t to get 12t.

−21t^2+12t+49−16

Subtract 16 from 49 to get 33.

−21t^2+12t+33

Swap terms to the left side.

33+12t−21t^2

I hope this helped!

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<h3>Answer:  C) 5</h3>

==========================================================

Work Shown:

s = square side length

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A = s^2

A = (ax+b)^2

A = a^2*x^2 + 2abx + b^2 .... apply the FOIL rule

A = 9x^2 + 12x + 4

Equating corresponding terms, we see that,

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Using a = 3 and b = 2, the sum of the values is a+b = 3+2 = 5, so that's why the answer is choice C.

Side note: 9x^2 + 12x + 4 factors to (3x + 2)^2

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