Question

please answer these questions with solutions​

Answer 1

Answer:

(i)x²+10x+25

x²+2×5×x +5²

( x+5)²

(x+5)(x+5)

(ii)x²-20x+100

x²-10x-10x+100

x(x-10) -10(x-10)

(x-10)(x-10)

(iii)4x²+12xy+9y²

(2x)²+2×2x×3y+(3y)²

(2x+3y)²

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

(iv)a⁴-10a²b²+25b⁴

(a²)²-2×5b²×a²+(5b²)²

(a²-5b²)²

(a²-5b²)(a²-5b²)

(a+√5b)(a-√5b)(a+√5b)(a-√5b)

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Answer 2

Qᴜᴇsᴛɪᴏɴ :-

Factorise

1. x² + 10x + 25
2. x² - 20x + 100
3. 4x² + 12xy + 9y²
4. a⁴ - 10a²b² + 25b⁴

Sᴏʟᴜᴛɪᴏɴ :-

( 1 ) x² + 10x + 25

⟹ x² + 2 × x × 5 + 25

⟹ x² + 2 × x × 5 + 5²

⟹ (x + 5)²

( 2 ) x² - 20x + 100

⟹ x² -2 × x × 10 + 100

⟹ x² -2 × x × 10 + 10²

⟹ (x - 10)²

( 3 ) 4x² + 12xy + 9y²

⟹ 2² x² + 12xy + 9y²

⟹ 2² x² + 2 × 2x × 3y + 3² y²

⟹ (2x)² + 2 × 2x × 3y + (3y)²

⟹ (2x + 3y)²

( 4 ) a⁴ - 10a² b² + 25b⁴

⟹ a^2×2 -2 × a² × 5b² + 5² b^2×2

⟹ (a²)²-2 × a² × 5b² + 5² b^2×2

⟹ (a²)² -2 × a² × 5b² + (5b²)²

⟹ (a² - 5b²)²