Question

HELLO


QUESTION: FACTORISE​

Answer 1

Step-by-step explanation:

$1)4 {p}^{2} - 9 {q}^{2} \\ \\ ( {2p)}^{2} - ( {3q)}^{2} \\ \\ apply \: identity \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ \\ ( {2p)}^{2} - ( {3q)}^{2} = (2p + 3q)(2p - 3q) \\ \\ \bold{4 {p}^{2} - 9 {q}^{2} = (2p + 3q)(2p - 3q)}$

$2)63 {a}^{2} - 112 {b}^{2} \\ \\ 7 \times 9 {a}^{2} - 7 \times 16 {b}^{2} \\ \\ 7(( {3a)}^{2} - ( {4b)}^{2} ) \\ \\\bold{ 63 {a}^{2} - 112 {b}^{2} = 7(3a + 4b)(3a - 4b)}$

$3) \: 49 {x}^{2} - 36 \\ \\ ( {7x)}^{2} - ( {6)}^{2} \\ \\\bold{49 {x}^{2} - 36 = (7x + 6)(7x - 6)}$

$4) \: 16 {x}^{5} - 144 {x}^{3} \\ \\ taking \: {x}^{3} \: common \\ \\ {x}^{3} (( {4a)}^{2} - ( {12)}^{2} ) \\ \\ or \\ \\ 16 {x}^{3} ( {a}^{2} - ( {3)}^{2}) \\ \\\:\bold{16 {x}^{5} - 144 {x}^{3} = 16 {x}^{3}(a - 3)(a + 3)}$

$5) \: ( {l + m)}^{2} - {(l - m)}^{2} \\ \\ (l + m + l - m)(l + m - l + m) \\ \\( 2l)(2m) \\ \\ \bold{( {l + m)}^{2} - {(l - m)}^{2} = 4lm}$

$6) \: 9 {x}^{2} {y}^{2} - 16 \\ \\ ( {3xy)}^{2} - ( {4)}^{2} \\ \\ (3xy + 4)(3xy - 4) \\ \\\bold{ 9 {x}^{2} {y}^{2} - 16 = (3xy + 4)(3xy - 4)}$

$7)( {x}^{2} - 2xy + {y}^{2} ) - {z}^{2} \\ \\ since \\ \\ ( {x}^{2} - 2xy + {y}^{2} ) = ( {x - y)}^{2} \\ \\ so \\ \\ ( {x - y)}^{2} - {z}^{2} = (x - y + z)(x - y - z) \\ \\\bold{ ( {x}^{2} - 2xy + {y}^{2} ) - {z}^{2} = (x - y + z)(x - y - z)}$

$8) \: 25 {a}^{2} - 4 {b}^{2} + 28bc - 49 {c}^{2} \\ \\ 25 {a}^{2} - (4 {b}^{2} - 28bc + 49 {c}^{2} ) \\ \\ 25 {a}^{2} - ( {(2b)}^{2} - 2(2b)(7c) + {(7c)}^{2} ) \\ \\ {(5a)}^{2} - ( {2b - 7c)}^{2} \\ \\ (5a + 2b - 7c)(5a - 2b + 7c) \\ \\ \: \bold{25 {a}^{2} - 4 {b}^{2} + 28bc - 49 {c}^{2} = (5a + 2b - 7c)(5a - 2b + 7c)}$

Hope it helps you.

Answer 2

Step-by-step explanation:

refers to the attachment