Question
20) \( (2 t+7)^{2}= \) 21) \( 19 a^{2}-64 b^{2}= \) 24) \( (3 x+4 y)^{2}= \) 23) \( \left(4 m^{2}-7 a\right)^{2}= \) 24) \( (3 p+4)^{2}= \) 26) \( (3 a-56)^{2}= \) 26) \( (6 x+y)(y-6 x)= \) 27) \( 144 a^{2}-121 c^{2}= \) 28) \( (15 x-y)^{2}= \) 29) \( (2 a+y)^{3}= \) 30) \( 9 a^{4}-16= \) 31) \( \left(10 a^{3}+b^{2}\right)^{2}= \) 32) \( (5 x-2 y)^{2}= \) 33) \( \left(4 x^{2}-2 y\right)^{2}= \) 34) \( 16 x^{2}-25= \) 35) \( (10 p+7)^{2}= \) 36) \( (4-5 m)^{2}= \) 37) \( \left(8+4 a^{2}\right)^{2}= \) 38) \( \left(a^{3}+3 b\right)^{2}= \) 39) \( 36-9 x^{2}= \) 40) \( \left(6 p^{2}-8 q^{3}\right)^{2}= \) 41) \( 9 m^{2}-16= \) 42) \( \frac{1}{4} a^{2}-16 \) 35
Ask by Campos Newton. in Russia
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (10p + 7)^2 = 100p^2 + 140p + 49 \)
Solution
**35) \( (10 p + 7)^{2}= \)**
Раскроем квадрат бинома по формуле \((a + b)^2 = a^2 + 2ab + b^2\):
\[
(10p + 7)^2 = (10p)^2 + 2 \cdot 10p \cdot 7 + 7^2 = 100p^2 + 140p + 49
\]
**Ответ:** \(100p^{2} + 140p + 49\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
When you're tackling polynomial expressions like these, it's really handy to remember some fundamental algebraic identities, such as the square of a binomial \( (a+b)^2 = a^2 + 2ab + b^2 \). This will help you simplify expressions quickly and accurately — just plug in your values! Another fun tip is to think of polynomials as expandable treasures! When you encounter something like \( (3p + 4)^2 \), imagine having 3 p’s and 4 cookies; how many combined treats do you end up with? Use those toothsome visuals to help remember the steps in expansion. 🍪
